The gum wrappers are kept in a box under his bed.
The first year he leaves it where it has always been, but when he comes back the box is gone. He cries himself to sleep for a week and can barely eat more than a few bites.
Second year, he takes it with him, hidden at the bottom of his trunk. But it feels wrong to have with him, what if someone asked about it? What would he say? No one seemed to know about his parents. He can never bring himself to open it.
Before third year he buries it out in the garden, under a hedge, thinking it was the only place she would not be able to find it. When he comes back at the end of the year, the box has gotten damp with mud and water and something had eaten through half the wrappers. He is devastated.
He spends the entire summer making a wooden box with his hands and learning a spell that will keep it shut against intruders. He puts it in the closet this time and feels confident as he goes off to school. He returns to find it on his desk, open and empty, with a note telling him not to keep such clutter around. It is the first time he really yells at his grandmother. They don't talk for a week.
Fifth year he asks his uncle to hold onto it. He mumbles a bit about it being something his grandmother can't see and his uncle laughs. It is clear he thinks it's some sort of girly magazine. For the first time it is returned to him whole and intact.
By sixth year he thinks he has perfected the charms on the box, but just in case, he pries up one of the floorboards and hides it under there, covering the spot with his rug. It is the first thing he checks when he returns home. It is there. He goes through and touches each wrapper, counting. They are all there. He has never felt more relieved.
After the battle, he stands in the middle of the great hall, looking at the people and the rubble and he doesn't know what to feel. This is what they were fighting for. Each gum wrapper a monument to this moment.
He gets out the box when he returns home and sits on the bed with the wrappers around him. They should have been there. He wants them to know that their sacrifice has finally been repaid. That everything they gave up has been worth it, after all these years.
There is a knock on the door, and his grandmother does not wait for him to admit her. She holds a box, an old shoe box that he almost does not recognize. She opens it, and inside are the wrappers he thought he lost, all those years ago. She pours them out onto the bed before sitting herself, staring at the wall determinedly.
"I did not want you to have a sad childhood."
He reaches to hold her hand, but she moves away from him and stands. Emotions have never been her strong point.
"I have an idea," she states, and he expects her to go on. But she starts separating wrappers, one in the wooden box and one in the shoe box. He assists and soon every one has been sorted. She takes the wooden box, the one he made, and asks him to come with her. Confused, he follows her to the fireplace. A bit of Floo powder and they arrive in Hogsmeade; he has to run to catch up to her, a woman on a mission.
The castle looms before them, but not like it did his first year. It's a carcass of that castle, gaping holes and missing towers ominous. He's similarly awestruck, but it sinks his stomach rather than opens his eyes. It is not the castle he went to school in, it is still a battleground. The air might not crackle with active magic anymore, but the fighting can still be felt. He hopes they can get rid of it before Hogwarts starts again in the fall; this is supposed to be a place of safety, not war.
They sidestep the entrance to the castle, and head off into the grounds. He almost runs into his grandmother when she stops short.
She looks around and holds out the box. And he understands, a rare moment when him and his grandmother are on the same page. This was a war that encompassed all the generations of Longbottoms living.
They have no shovel, so he digs the hole magically and buries the box by a tree. From the spot he can see Gryffindor tower, and he thinks he can see his dormitory, the spot where he grew up constantly thinking of these gum wrappers.
He doesn't mark the site. There isn't a need. He won't forget.