Originally Posted by
twospoons
There isn't a way to delete accepted gifts, but there's no limit on the parts you can receive so it's not like you'll run out of space. (Technically you can receive up to 32000ish parts, or 32000ish of each individual part or something like that--high enough that it's not really a limit, anyway)
If it just bugs you on principle (me too!) console yourself with the thought that maybe the next appliance to be built will require those old spring leaves or wagon wheels or whatever, and you'll be ahead of the game in building them! That's why a lot of players just accept all gifts when there's nothing new to be built, they want to be ready for anything.