Repair or clean a CD?

Wife put favorite music CD's in a car visor holder. Now they all have a "plastic/rubber" stripe where they came in contact with this cheap Chinese plastic. All giving format error messages. Any help? Cant find a more "correct" forum.

 

I use a good car polish (not wax) and as plodr says rub from the centre to the outside edge and not in circles around the disk (this is important).
Another trick is a quick spray with Mister Sheen furniture polish or Glitz furniture polish and then wipe with a tissue of soft rag.

If neither of the above work for me then I consider there is nothing to lose and then I use automotive cutting compound (fine) and rub from the centre to the outside edge until the entire surface has lost its shine and is an even matte surface. Then I use the car polish again to restore the shiny surface.

If the disk is really important then I also use Plexus plastic and plexiglass polish prior to using the cutting compound. Plexus can only be used with a soft cotton cloth and not paper towels, tissues or any synthetic material. Plexus is primarily used for polishing the canopies on fighter jets and other aircraft with plexiglass windows. Make sure you use it in a well ventilated area. Oh and the reason I don't use Plexus first is because it is so damn expensive