Rey is still a scavenger at heart and always finds little things to give to Kylo. She leaves them in different places around the house she knows he'll find them in. He finds all kinds of weird stuff, from little pieces of scrap metal that she thinks are shaped like things (hearts, dogs, ewoks, etc) to rocks she finds that she thinks he'll like to pretty leaves and flowers. He keeps them all in a drawer and Rey tears up a little when she stumbles upon it and finds that he keeps them all.
Oh you know he would totally keep everything that she ever gifted to him. This is the most adorable headcanon. Thank you anon!!!