I'm sorry, I can't help you remove scratches, but I can help you avoid more....
For my D1, I use PVC shrink wrap bags. You can buy them by the 100 on Ebay. Make sure you get PVC bags; they are more durable.
The bags require some modification after they are shrunk, but they work great. My D1 remote looks almost new (the felt pads on the buttons raised them for easier activation).
I placed one on the D2 when I got it and it works the same except the charging plug and Tether must have a cut out.
It will certainly protect the screen and keep the dirt out.
If you decide to go this route, here are some helpful instructions.
Use a heat gun. They can be purchased for around $10. Cotton gloves are very helpful in handling the controller and bag during the process.
Place the remote all the way in the bag face down on a bench/table and center it side to side.
Sweep the heat gun over the controller and bag. Don't leave the heat gun in one spot or be to aggressive with the shrink.
Once it has pulled somewhat tight, turn it over and do the face while everything is still warm. The front will tighten up leaving it without any wrinkles in the face. Remember, don't be too aggressive with the heat, you will melt/tear a hole in the bag and will have to start over.
Once front and back are shrunk, work the heat over the edges so the bag pulls nice and tight. It takes a little finesse, but you shouldn't waste more than 2 bags figuring it out.
After the bag is shrunk, use a razor knife to cut out for the stem attachment. On the D2, you will have to cut out for the power connector also.
I trim the excess bag at the bottom (D1) to keep connectors accessible. I can go on probably 25-50 hunts before I have to replace the cover on the D1.
I have no idea how the power connector is going to affect the cover longevity on the D2.
The shrunk bag peels off very easy leaving a clean unit to recover.