Wash the stainless steel with warm, soapy water. Remove any food residue or dirt.
Rinse with clear water, removing all soap residue. Wipe dry with a clean cloth.
Moisten a soft cloth with club soda. Rub the soda into the burn marks with a circular buffing motion. Wet the cloth with more soda as necessary so it doesn't dry out as you clean.
Buff the stainless steel dry with a clean, soft cloth. The soda removes the burn stains, and the soft cloth brings out the full shine of the stainless steel.