Let the stove cool completely. Never attempt to clean a hot stove as you can burn yourself.
Soak a plastic scrubbing pad in water.
Press the pad onto the stainless steel surface and rub in the same direction as the grain on the stainless steel. Make one stroke and examine the stainless steel to determine if the scratch is gone.
Continue until the scratch is completely gone or until you can't lessen its appearance any more.
Apply one drop of stainless-steel polish to the scratch.
Scrub the polish into the scratch until it is fully blended with the stainless-steel surface.