Mist water onto the scratch marks. Sprinkle baking soda over the scratches.
Spritz glass cleaner onto the baking soda. Scrub the affected areas with a sponge until the scratches are gone. Rinse the sink with clean water and repeat this process as necessary to remove all of the scratch marks.
Sprinkle the scratches with a heavy coating of baking soda if the scratches remain. Cover the affected areas with paper towels and plug up the sink.
Spray hydrogen peroxide onto the paper towels so they are soaked. Let them set until they are dry.
Take off the paper towels. Wipe over the area with rag, then rinse the sink with clean water.
Apply enamel paint to the scratches if they are still there. Clean the area well with rubbing alcohol, then dry it thoroughly. Dip a small artist’s brush into the enamel paint and apply it lightly, working from the center of the scratch toward the edge. Let it dry for at least one hour, then sand lightly with fine-grit sandpaper. Apply another coat of the paint.