Wait a baseball cap?
Don't spoil it how to get it!
And you can destroy the medal?
You can destroy it - I also destroyed it, accidentally. If you find it in your inventory, then choose to inspect it, Claire notices it's actually a gold coin attached to string (or something), and you can choose to take it apart (destroying the medal and giving you 1 coin) or keep it. I wish I hadn't destroyed it, but maybe you won't :D