Mo could have put the box in the trunk of the car, or in storage with all his other belongings but he chose to keep it close despite the pain it brings him. Which might be an allusion to how he feels about He Tian. You bring me so much pain but tossing you aside would have hurt me even more. I can't tuck my memories of you away with everything else cause they're precious to me, you're too precious to me…
When it came to the box of memories Mo had the option of avoiding the pain, choosing when he wanted to confront his feelings and taping it up when he didn't want to anymore.
But now that he's living with He Tian there's nowhere to run. He can't pick and choose when he wants to see He Tian. He Tian didn't give Mo a choice in the situation.
Mo is literally being thrusted into everything he's been trying to ignore. He Tian's presence, He Tian's space, He Tian's lifestyle etc.
It's going to be hard for him to keep up the detached facade now that they're going to be around each other all the time. It's going to be harder for him to lie to He Tian about how he feels. Mo probably wouldn't feel comfortable hurting He Tian with his words in his own home.
It'll most likely be his breaking point and the last hurdle he has to overcome to let himself be fully vulnerable with He Tian.
I hope they talk about it although I can see Mo coming to terms with it on his own and gradually becoming softer with He Tian.