Baking soda is quite effective in removing light scratches on stainless steel. It has a powdery texture that serves as a gentle abrasive. Add water and baking soda to make a paste, put it on the surface of the metal, and scrub lightly. Then wipe off the baking soda and wipe the surface with a damp cloth. This is most effective for light scratches. You may need something a little more substantial for more significant scratches.