Uninstalled parts go to the inventory (the suitcase). There, they are universal parts, ready to fit any car (or be gifted to a friend). You have to assign them to your current car, then install them in the preparation menu (tuning).
Is it not possible to remove upgrades from one car and place then on another? I uninstalled a few and they don't appear in the suitcase or other cars tuning menus.