This is what I use.
It has an abrasive wheel but it's extremely fine grit. You spray it some water (comes with a spray bottle) and just pop it in. If it's a scratch you can clearly feel when you run your finger over it, you'll have to run it through a few times.
If after say 6-8 passes, there's no improvement, then you're probably fucked.
As you may know, the data is on a metallic layer just under the label, so if the label side is scratched, again, assume the position.