Smear a little white baking soda toothpaste over the scratch on your crystal. The toothpaste should fill the scratch and a little of the area around the scratch.
Rub the toothpaste into the scratch with a soft eyebrow brush, moving in circular motions. Don't press down hard. Use a firm touch but not so firm that the bristles bend. Work up and down the scratch for a minute or so.
Dampen a soft cloth with warm water, and rinse away the toothpaste. If the scratch is still there, apply more toothpaste and rub it this time with the cloth. Using the eyebrow brush again may cause more surface scratches. Continue rubbing until the scratch disappears.