You decide to bring it with you, for luck, so you captchalogue it with your ALLEGORY MODUS, swapping it for a pair of mittens that have been stuck in there since winter ended, on the basis that they're both intended to provide warmth and comfort.
Adding new items to your sylladex is pretty easy because you can just pick them up and take them, but lowering the total number of items requires finding an object that metaphorically stands for "nothing" so that you can swap it out without putting something in. You try to only put things in if you can take something out at the same time, which means you mostly just end up carrying things in your hands like a schmuck from the pre-angelic age.