Back when Clementine lost her hat in Season 1, she seemed upset that she lost it but not as if she couldn't live without it. Fast forward to where we are now in Season 2. Clem has gone through a lot with her hat always being there. Assuming that everything she had in her backpack is no longer there (it seems as if it is empty), her hat is the only memento of the good and bad memories of her life so far. How would you feel if Clem has the choice of either keeping her hat or leaving it behind at the end of the season? If you keep it, she'll say it's because of all the memories it holds and is a token to remind her to never give up hope and survive. If you leave it behind, she'll say it's because the memories it holds are a burden and that she needs to leave these burdens behind in order to begin anew and survive the apocalypse. If you time out, her decision will be based upon you past action i.e. whether you expressed interest in looking for it as Lee, whether you kept her hope alive about finding her parents, whether you killed or left Lee and Sam, and other gaming choices that relate to your outlook of life and hope. If you didn't play Season 1, you're Season 2 choices will be the main determining factors. I feel like if this was choice in the game, it may actually be a harder choice than people may think, especially if the reasoning for keeping and leaving were known/stated right before the decision prompt.