Regardless of how careful people try to be, time and use result in scratches on stainless steel appliances. Removing the scratches can take a bit of elbow grease, but these scratches do not have to be a permanent annoyance.
Step 1 - Buff out the Scratch
Use 80 to 120 grit sand paper or Scotch Brite scouring pads (first gray, then maroon) to buff out the scratch. Always buff with the scratch or the markings will become much worse. If this doesn't work or sandpaper makes you nervous, try Step 2.
Step 2 - 3m Liquid Compound
Use a green Scotch Brite pad to apply 3M liquid compound designed for cars. Always rub in the direction of the grain. Multiple coats might be necessary. If the liquid compound can't be found, try Step 3.
Step 3 - Revere Copper Cleaner
Apply Revere Copper Cleaner with a soft cloth. Do not use the circular motion directed on the package; rub with the grain of the steel. Wipe the Revere off and apply vinegar around the steel to remove the greasy residue. Multiple coats may be necessary.