How can I  repair scratches on a coated stainless steel surface?
I looked into this some and there is no easy answer. Appliances are a 4 ( brushed) finish,BUT different mills may supply slightly different appearances. It is close to a 120 grit finish. I have four SS appliances , 3 different manufacturers all 
Korean but the finishes do not look identical .I doubt there is a coating. Mine all all non-magnetic SS ( " 18-8" or 304 ). When I was shopping I found 90 % of the US manufacturers use magnetic SS ( 13 chrome ).Again the alloy will not significantly affect the appearance. I tried rubbing a hidden spot with 180 silicon carbide paper and it polished ; it was too fine. I then tried 150 sand paper ; still too fine. A "net" site said the finish should be equivalent to 120 grit ; that sounds like a good possibility . I don't think any coating is significant .  Summary : Try 120 grit paper.