I had to recently replace my number plate holder - it was held on by self tappers, not rivets. I'm surprised at the rivets being used! I'm looking at a full bumper respray shortly and will be filling & flattening the number plate area with the surround removed now after seeing yours - that really was a shocking job.
Not sure how I'll fix the surround back on afterwards - the bumper is too curved for putting the numberplate straight on, but I don't want the surround screwed on. I don't think pads are the answer though (due to limited contact area on the surround) ... how are you planning to fit it back on Z4 Coupe, ?