Clean the surface of the tile with a household spray cleaner and a cloth.
Dampen a cloth with lacquer thinner, dab the scratch and let it dry overnight.
Apply a thin layer of liquid seam sealer from the bottle tip to fill in the scratch. Again, allow the surface of the tile to dry overnight.
Sand the surface with fine-grit sandpaper to level the surface.
Apply a thin layer of vinyl floor finish to the repaired surface. Vinyl finishes are usually available in high-gloss and matte finish. Choose the finish that matches your surface. Wait an hour for the finish to dry and apply another coat. Allow the finish to dry overnight.