Pour 1 cup of vinegar into a bowl. Dip a clean rag into the vinegar and wipe the marks from the stainless steel refrigerator. Press the rag hard to remove stubborn burn marks.
Sand away the burn marks using a piece of 100-grit coarse sandpaper. Run the paper in a downward fashion, along the length of the grain or finish, from top to bottom. Buff with a soft cloth.
Scrub the burn marks with the rough side of a scouring cleaning pad. Run the pad in a single downward motion, keeping in line with the direction of the grain. Wipe the scoured area with automotive liquid rubbing compound using a clean, lint-free cloth. Attack the marks again with the scouring pad and repeat with the rubbing compound until the marks disappear. Wipe the area down with white vinegar to clean the compound away.
Clean the burn marks with a commercial copper and stainless steel cleaning solution on a clean, lint-free cloth. You can find this solution at specialty cookware shops or home improvement stores. Follow the manufacturer's instructions for amount to use.