Their first signifiant interaction was in chapter 47, during the pool arc. Anime-only fans missed a few cut sentences who are interesting : it is implied that Terasaka have been quite observant, at least in Itona’s case, given how he noticed small barely visible changes. But the important part are Itona’s words to Terasaka : that he’s weak because he have no vision. 

Now, skip a few page...

...And you have Terasaka calling the class ‘weak’ and saying how he have vision. As Nagisa notices, those aren’t Terasaka’s own words. What Itona told him must have been quite impactful on him, enough to change his speech.

But, by the end of the arc, Terasaka wins against Itona ; with the help of Karma and the whole class, sure, but it’s not like Itona wasn’t acting according to Shiro’s plans anyways. The strength and build that Itona had implied were useless enabled him to hold onto a tentacle for the chemical to kick in, but the more important point : Terasaka admitted he was an idiot who could get easily manipulated and he needed Karma to comes up with a plan. In a way, he admitted he was weak and needed help, and that what led the class to victory. It’s a battle of ideal, and it’s also why it had to be Terasaka and his gang who saves Itona later.

Between chapter 49 and 87, though, a lot happens. Terasaka have been getting closer to the other members of class E, notably to Takebayashi. And then there’s the Island Arc. Let’s take a closer look at chapter 69 : we learn that Terasaka is also ill, but still choose to come and help. Given what he said previously during the arc (”Who do they think they are, messing with people’s friends ?”) and how his Roll Book profile’s treasured items is : ‘Best friends’ (I swear this guy is too cute), the fact some of them will die should be enough of a motivator, but we can learn of another reason : 

Guilt. Terasaka still feel really bad about the pool incident (which is kind of normal, given that, well. He almost killed the whole class. Well 7 or 8 according to Shiro’s predictions but, that’s, like. A lot.) He wants to redeem himself, and by the conclusion of this arc one could say he is fully redeemed, but whether Terasaka thinks this is the case is unclear. But, you know what would help him ease this feeling ? Having someone in a similar situation (a former antagonist who had a part in a plan which might have killed multiple students) also integrate the class.

In Terasaka’s Roll Book profile, there’s this line at Itona’s paragraph : Seeing Itona reminds Terasaka of back when he didn’t get along with the class, so he volunteered to look after him. Terasaka sympathised with Itona’s situation, which made him wants to help him.

Note that he’s the first, when the class confront Itona, to tell him they will all forgive him (which he should know best, after all). 

So, chapter 87. The whole Terasaka gang unite to try to makes Itona change his way of thinking. The whole chapter is honestly super cute in a dumb way, which kinda describe this group well. Frankly even without talking romance this team is a family and you should love them.

But Itona still is focused on victory and becomes berserk, which makes the whole group run away :

Except for Terasaka. Now, this guy isn’t that brave (look at the first chapter. Look at his reaction in front of black Korosensei), but when it comes to people he cares about, he’s willing to endure quite a lot (the tentacle during the pool incident and walking with high fever during Island Arc are proof). He cares about Itona, because damnit that guy is being an idiot like he himself was before and he needs someone to set him straight, and if Terasaka got that someone, there’s no reason Itona shouldn’t get help too. 

This whole chapter is important for Itona, being saved from the tentacles. But it’s also important for Terasaka, because it brings closure to his whole character arc, from the delinquent isolated from the others to a full member of class E who can help others due to his past experience. It does bring a special deep to his relationship to Itona. 

Now, at this point you might see we spoke a lot of Terasaka. Well, let’s talk about Itona : his backstory start as the father he loved so much ran away from his debt, abandoning his child. It is mentioned that Itona goes live with his uncle, that we never see, and we can suspect of neglecting his nephew. Then, he met Shiro, who becomes his legal guardian... and who seemingly leave him to die as part of his plan. Which from a logical appeal was brillant to trick Korosensei, but from an emotional point of view, is really a jerkass move. You bet after all that Itona must have abandonment issues. (And that makes his inclusion in class E all the more important, because here, give that child a big found family).

Now, this is more of headcanon territory. But by the time Itona fight with his former comrades, he was already abandoned by his father (which is the reason of the fight). We don’t see much of Itona’s character while his father was still there, so we don’t know if he was as foul mouthed. But it is frequent, though I don’t know how much, for people suffering from abandonment issues to hijack their new relationships by “pushing them away”. As Itona don’t seems to present other signs of an abandonment issue (which is curious, but I understand why Matsui couldn’t or wouldn’t talk about it, though it would have been nice if it was acknowledged), this is truly more of an headcanon that this is the origin of his foul mouth and why he keep insulting the people he’s the closest to (well, the people or their ramen).  It would make the second part of his paragraph in Terasaka’s profile more meaningful, though : Seeing Itona reminds Terasaka of back when he didn’t get along with the class, so he volunteered to look after him. As a result, Terasaka became the best excuse there is for Itona to bring out his venomous tongue. Well, wether this is true or not, having someone like Terasaka by his side, who won’t mind too much his rude language and who will stand up against danger when it’s for his friends, would be important for Itona.

Note that the relationship between those two do progress : look at chapter 88, when Itona just became a true student of class E

He’s laughing along with everyone, and it’s super cute and all, but he does try to keep Terasaka away a bit.

(In the manga at least. In the anime, he’s just happy from the situation.

Seriously this is too cute. Who permitted Lerche to make him this cute.)

But, in chapter 122, when Karma talk about everyone’s talents...

Itona doesn’t seem to mind at all. Or even care. (And since this panel is about Terasaka, Matsui could have drawn him with anyone else. Though I guess it makes it more visually interesting given how Itona is the smallest of Terasaka’s friends (excluding Hazama but I’m pretty sure anyone who touch Hazama like that is cursed for life). I mean, they have a 20cm difference between them. It’s more than between Karma and Nagisa. Actually the only reason Itona keep Terasaka around is because he can reach the higher shelves for him.)

And then there’s that moment, in chapter 126, where we see three group of friends, Sugino+Nagisa, Maehara+Isogai (with Okano in the background), and Terasaka with Itona. Given how the first two are quite strong friendships, it says a lot about the third. (And there’s the whole thing with the text, which is why I’m just putting a link instead of making this post even longer with overanalysis).

There’s another moment that I think is precious : during the Shinigami’s arc, when the two other groups of students have fallen, Terasaka is more than ready to fight Shinigami and is understandably a little angry :

But after Itona’s reaction (and telling him it’s a dumb idea)

Terasaka’s doesn’t seems angry anymore, just confused

And that’s the moment Itona says it’s okay to lose this battle and they have to wait for the right chance to win someday (which is a bit silly because we’re talking about the best hitman in the world, who talked previously about keeping them hostage and maybe kill one or two of them). Like, the whole situation is a parallel to chapter 87, with calming the angry guy who wants to fight by saying “you’re being dumb and you will lose like this, let’s win another day” (and the no-longer-angry guy realising that yes, that was dumb), but the roles are inverted. They both can help each other in realising their mistakes. 

Also, while we’re on this arc. There’s this bit in chapter 103 :

Which seems absolutely like Terasaka jumping ahead, because he might be the strongest in the class, and Itona isn’t that far at that point of the story with his body modifications still a bit there, but they can’t be better than a whole team. But it’s not without basis : look at the Volume 16 rankings in knife technique, both solo and duo. The top places in duo techniques are occupied by the same people from the solo techniques, but in 4th and 5th place, we have Terasaka’s gang, who in the earlier months were slacking in PE. Keep in mind that when Itona joined the class, he was months behind in the training (because he used tentacles instead of knifes and guns), and his high ranking in the long distance categories is probably due to a remain of kinetic vision. Besides having strong bodies, they four of them must have excellent teamwork. They probably worked a lot together (which explain how in the class war and in the final arc, they work as a group).

In conclusion, Terasaka and Itona have a deep relationship, and overall the whole Terasaka team have very strong bonds. 

...And as a bonus, if you want to ship them romantically, imagine Karma after the kiss between Nagisa and Kayano, coming back to his favorite victim.