Scratched Up NGC Case

Try rubbing it with toothpaste on a cloth. I don't know what the grade of toothpaste is, unfortunately. Don't dilute with water.

10,000 grade tin oxide from a lapidary supplier is the best way to go. 10,000 grade is fine enough not to leave a haze behind on the plastic case. This comes in a white powder form and would be used as a watery paste, when mixed with water.
The case needs to be waterproof, or you will get capillary flow into the slab.

The grading system here is the same used in the automotive repair industry paint shops.

I use up to 100,000 grade diamond polishing paste to obtain a superfine polish, when cutting yellow sapphire.

The product that I use is called Novus.
Comes in three bottles:
-- heavy scratch remover
-- fine scratch remover
-- plastic clean& shine

You have to supply the fourth element -- elbow grease.

It works well BUT some scratches are too deep for even the "heavy" to handle.