The store items are Sims3packs stored by default in your Downloads folder. Just open the folder and delete whatever you don't want (or, alternatively, move it to another location for safekeeping). There is also an uninstall button in the launcher ~ I assume this is what is not working for you when you refer to the error.
Deleting stuff from the Downloads folder doesn't remove it from the game, only from the list of Downloads. I have done this before (mostly by accident) and the items still show up in-game. I think I would need a way to selectively edit the dbc files in the DCCache, but since the individual file names would make no sense anyways, I'm not even going to bother figuring how to go about that.
I guess I'll just have to wait for the eventual community supplied launcher replacement and put up with a cluttered game for now.