I have kept all of my decorations although I don't have room for them and don't even like many of them, but they kind of serve as a reminder of previous events. Plus I'm kind of a hoarder, so it's hard for me to let go of things.
I would, however, **love** to be able to trade our left over materials for some sort of currency, whether it be gold, boosts, food - anything but coins! I really wish that they would let us exchange our materials for something. There is no way to dispose of it, unfortunately.