In a pinch, you can use a wet piece of toilet paper or paper towel. (Make sure that it is soft and not the slightly abrasive ultra-cheap stuff. )

Baking soda toothpaste is recommended.

Never apply the toothpaste in a circular motion. It scratches the disk furthermore.

Get a dry cloth and add a small amount of car polish to it, such as T-cut. Rub in circular motion for 15-20 minutes, then wipe dry. Or, use some cotton buds put a tiny drop on to the cotton bud and then wipe the disk in a circular motion. This works for any dust scuff marks from where the disk wobbles in the tray, when the Xbox is upright or moved.

Put a dab of peanut butter on a lint-free cloth. Rub it in a straight motion. The oils in it should help to repair scratches. Try it in the Xbox console again.