The back of iPod Touch devices are notorious for getting scratched.
I put mine on a table for a second, and when I picked it up there was a long scratch. Couldn't believe it.
Mine is very scratched now. I recommend you first write down the information on the back of your iPod to paper, there should be an ID or code that is unique to the device which you'll need.
You could try the ol' "brushed steel" look by scratching the metal in a vertical direction to create a lined pattern.
Only other option is to replace it with a new cover which isn't worth it if you bought it second hand. There is no magical way to restore the metal to look like new, the scratches are embedded into the metal. You can't just wipe them away. If you did remove the first layer where the scratches were you would still end up with a matte coating.