Here's a great way to remove light scratches and even some deeper scratches from GC jewels.
If your Jewel is heavily scratched / has deep scratches, it's advisable to do this:
Thx for the hint, SouLSLayeR!You could also let a very high grit sandpaper (more than 1500) make the heavy job of getting rid of the deep scratches, and then finish up with brasso.
Takes less time.

Just don't get too carried away with sanding, or the top of the jewel won't be flush with the rest of the drive lid.

This method does NOT work on the sticker-type jewels like the IcedCube ones. It'll only make them dull.
What you need:
- Brasso metal polish
- microfiber cloth (one is good two are better)
- "elbow grease"
- patience

WARNING: Brasso has a VERY strong odor and isn't exactly healthy to breathe in (may cause drowsiness and dizziness).
Also it's toxic to aquatic organisms, so don't empty it into drains. If you can, work outside. If you can't, work in a very well ventilated area.
If you plan on reusing the cloth, store it in a sperate box or in a somewhat airtight container.
DO NOT put it in a washing machine unless you want your clothes to smell like rotten eggs and gasoline.
Where to get Brasso? Well, that's a bit of a tough one... I'm from Germany and I got it from here, in the US it should be available in any hardware store or Walmart.
I don't know how or where to get it in other countries, but if you have the chance to obtain it at a reasonable price, go for it!
Allrighty the procedure itself is very simple but requires a lot of patience and "elbow grease".
Lay the cloth on a sturdy, even surface and dab a few drops of Brasso onto it.

Lay the jewel on the brasso and start by rotating it in a circular motion while gently pushing down.
Repeat, repeat and repeat until your fingers hurt

Brasso basically works as a sort of high-grit sandpaper, which means it scrapes off the plastic, layer by layer until the surface is even again.
This is a slow process so get ready to spend some time on this. (actually it's not that bad, my jewel took about 20mins to finish)

Check every 5-6 minutes for results by wiping off the brasso remains with a clean cloth.
Repeat until the scratches are gone / you're satisfied. This can take a VERY long time depending on how thouroughly you do it.
When you're done you should wipe away all the brasso remains and maybe clean the jewel with a bit of water. And TADA!! Scratch-free jewel!!
Obligatory before and after images, YAY!

Before


After

The camera literally had no more scratches to focus on, so it focused on the lamp

Well, that's it! Enjoy!! Feedback always appreciated!