Finish by applying a stainless steel cleaner/polish. This technique will also work for removing scratches from stainless steel sinks. If you're looking for an all-in-one scratch remover ...

On the flip side, the Hope's Perfect Stainless Steel Cleaner and Polish ($16) is specific to stainless steel items and sinks. This extremely easy-to-use cleaner is streak free and self-polishing.