Toothpaste is the answer....
and don't laugh.
There are quite a few ways to remove scratches depending on the severity of scratches.
Once you have tried rubbing alcohol and that does not work. You need to try a very small quantity of toothpaste and very soft cloth, preferable a sof chamois and buff the disk for some time and then wash it off.
The best method is get a buffing wheel - the kind that you get for car polishing. The softest one available is called "Swansdown" - sorry don't know where to get it. But any really soft buffing wheel will do. Use a plastic buffing compund lightly. Or some fine metal polishes like Hyfin work best.