Deeper scratches will require removing more material surrounding the scratch. Stainless is hard so without a motorized polisher it might be hard to do. If you own a device like a Dremel you could do it, if not a good jewelry shop can do it for you.
This. My SS casing is noticeably scratched but my screen is completely untouched, and I've had it hit so much things since I got it. It's been scraped along walls for God's sake and...nothing.