There's something so meaningful about Katniss associating Peeta with dandelions, especially when you take into account the way Peeta is viewed by others throughout the trilogy and how dandelions are viewed in real life.
Dandelions are considered by many people to be weeds. They're not toxic, but they're eyesores in any perfect garden or lawn; they spread fast due to the way they seed, so they're considered invasive; their one use—attracting pollenators—is negated by the fact that their pollen is low in nutrients.
In other words, they're useless. They're pests.
Peeta throughout canon is treated similarly. It's a repeated theme that he is always brushed aside and disregarded in some way, second best to someone or something else. He's the third son. His mother deems him inadequate, he loses to his brother in wrestling, his father always wanted a daughter. Haymitch saves Katniss over him in the first games, the rebellion saves Katniss over him in the Quell. Peeta, in the eyes of others, inculding himself, has very little value. It's partially why in Catching Fire he says on the beach, "Nobody needs me."
And yet, we see how Katniss views dandelions, just as she views Peeta. To Katniss, dandelions are a sign of spring, the first bit of food bees get after winter, a sign of cultivation and new life on the horizon. They mean being sustained, for every bit of a dandelion is edible. They represent hope. To Katniss, dandelions are beautiful.
Peeta is her dandelion. He takes a beating to feed her when she's starving. The bread he gives her is enough to keep her alive for when spring comes, and she can forage in the woods. At her lowest, most cynical, and most suicidal, Peeta returns to her and plants a garden outside her window so that she can mourn in peace, and bakes her bread for breakfast the next morning so she can eat. So she can live.
There is so much in the text that shows us how valuable Katniss finds Peeta. To her, Peeta is incredibly kind, talented, and intelligent. He's a wordsmith. He's her hope. He's beautiful.
But I think it's best expressed in Catching Fire, in response to Peeta's assessment of his worth: "It's true his family doesn't need him. They will mourn him, as will a handful of friends. But they will get on. Even Haymitch, with the help of a lot of white liquor, will get on. I realize only one person will be damaged beyond repair if Peeta dies. Me.
'I do,' I say. 'I need you.'"
To Katniss, Peeta is everything but a weed.
