Hi Kevin:
I doubt much can be done with this particular one. Some uncaring owner dropped a cigarette on the cover.
Novus makes a good line of acrylic polishes that does wonders for acrylic lids. Hairline scatches can be removed with patience. I've used this on my beogram 8000 and CDX lids. It's a two part formulation.
For deeper sractches that you can feel you need buffing wheels.
Let us know what you find.
Derek