After furniture or crafting stations like tables and anvils are placed is it possible to pick up and move them or are they stuck where you placed them forever? Same goes for some other background elements, like wooden platforms and walls. If you misplace them there must be a way to move or at least destroy them if they are in the wrong place.
You can use your Pickaxe to break placed objects.
Background walls can be removed with a hammer. You don't spawn with one, but you can craft a basic Wooden Hammer out of 8 Wood at a Work Bench.