I've never seen nor heard of any covering over the rear plate, glass or plastic. I agree with the shenanigans comment.
My favorite way to keep the plate from moving around is to stick some foam weatherstripping tape (hardware store stuff, usually about 3/16" thick) to the back of the plate. This will keep it from sliding around.
There are supposed to be three clips on the back, but the bottom one is often gone and the others tend to have the screws freeze up anyway.