Cosmetic Repair

You can try using an automotive polish/swirl remover then an automotive wax. I don't know what the chemicals would do to your particular plastic, so try it out first. I have found this effective to remove faint marks from automotive paint and plastics( such as mirror housings). These have a little grit in them which will scrub down the paint a little. I used to refurbish cars/jeeps, and used this to touch up my touchup work. You can use 600-1000 grit sandpaper for more extreme 'scrubbing'. These techniques may leave 'burn' marks where you have scrubbed out the texturing of the plastic. A less extreme technique would be to just use some softened canning wax in the scratch, then polish with some 'pledge' furniture cleaner. This is the safest, and probably what I would do.

i recommend you use a product specifically designed to polish plastics. a product i've found to work very well is plasticare. it's made in englewood, colorado. i live in colo and am able to buy it at a couple of well-stocked hardware stores or from the factory. don't know about availability in other areas. if you can't find this exact product, look for another designed to clean/polish pexiglas.

The polish you can get to remove scratches from Audio CDs should work here. It is plastic afterall. Discwasher makes a CD polish and scratch remover I have used successfully on damaged CDs.