I have been able to repair scratched cds before by polishing the scratch out.
Haven't tried the disk dr or such so I can't speak to their effectiveness.
Note:
If the TOP of the disc is scratched then scrap it, no amount of anything will help.
Step 1
Get a pencil eraser, the better quality eraser the better results.
and an CLEAN old t-shirt or something of soft cotton that is NOT terri cloth such as a towel and some high quality automotive paint 'cleaner'. I used McGuiars paint cleaner
Step 2
very lightly go over the scratch with the eraser in the direction of the scratch, and I do mean lightly. It is going to look terrible at this point but don't panic......yet
Step 3
Wet a small area of the cotton rag and buff out the area you just went over with the cotton rag you will have to buff it quit a bit to get it smooth again. alternate between wet and dry parts of the cloth.
repeat until it looks shiny again.
Try it and see if it works, If not then repeat the procedure until it does.