Apply a thin layer of nail polish to the scratch using the application brush. Allow the nail polish to dry for 5 minutes, and use nail polish remover to clean away excess polish. To remove excess polish, pour a dime-sized amount of nail polish remover on a clean cloth and wipe around the scratch.
Buff Brasso cleaner into the scratch. For tougher scratches, Brasso Multi-Purpose Metal Polish can reduce the appearance of the scratch. Pour three to four drops of the Brasso cleaner onto a clean cloth, and buff the scratch in a circular motion. Use a part of the cloth that doesn't have cleaner to wipe the scratched area. Repeat if the scratch remains.
Purchase a Janvil Glass Revive Kit. This kit is the closest you can get to professionally removing scratches without taking the tabletop to a glass specialist. The kit includes 10 items to assist you in safely removing scratches, including spray bottles, polishing disks, pads and polishing creams and buffing solution.
Take the tabletop to a glass specialist. If the scratch is too deep or requires intensive labor, have it repaired by a specialist to save yourself time and money. If necessary, the specialist may replace the glass.