Soak up as much of the hair color stain as possible, using a clean cloth. Work until the color no longer transfers to the cloth.
Wet the sink with water.
Sprinkle baking soda over the dye stain.
Scrub the baking soda into the dye stain with a scrubbing brush. Scrub in the direction of the stainless steel grain to prevent scratches. Work until the dye stain is gone or until it is as light as possible.
Mix 3 tablespoons of cream of tartar with 1 tablespoon of hydrogen peroxide.
Blot the solution into the dye stain until it is gone or no longer gets any lighter.
Apply a commercial stainless steel stain remover to the sink with a clean cloth. Rub it into the sink until the stain is gone or until it is as light as possible.
Rinse the sink with clear water.