This procedure isn't for anyone who's impatient. It has worked for me is polishing out scratches on glass doors (don't ask) as well as on watch faces. Ok, I'm obsessive.

You need a Dremel tool and jeweler's rouge - available at hardware stores in various grits. Depending on the depth and severity of the scratch start with the coarsest grit, as you would with sandpaper.

Use the Dremel with the polishing wheel and polish away, back and forth over the area, but not in any one spot. Back and forth, back and forth, grasshopper. Your wrists will grow tired.

Eventually you will see progress. Finally, it will work - as long as the scratch isn't all the way to the plastic.

Bob