Lightly run the pumice stone or non-metallic scouring pad over the surface of the door, following the natural grains of the stainless steel. Use long strokes, continuing in the same direction over the entire door to blend the scratched area with the rest of the door.
Coat the entire door with a stainless steel cleaning solution intended for cleaning pots and pans. Apply with the grain, let sit for a few minutes, then wipe it off.
Wipe vinegar over the surface of the door using a paper towel or soft cloth to clean any residue left behind. Buff the stainless steel door with a soft cloth.