Bar Keepers Friend is great for cleaning SS and removing some stains, rust, etc. It is very mildly abrasive and has a very weak acid, similar to citric acid, that is very safe to use. One of the things we use to remove
iron stains from pool surfaces, plaster and synthetics, is mild acids, like citric or asorbic acid, in high dose treatment into pool water. (Doesn't work for most other metal stains though. And can actually set copper stains.) Most grocery stores, around here, have it with cleaning products.
Amazon.com: Bar Keepers Friend® Cleanser & Polish: 12 OZ: Home & Kitchen
DO NOT USE BAR KEEPERS FRIEND ON: Gold, silver, pewter, marble, lacquered metals, or anodized aluminum.
I use it on my "manly salmon/pinkish" "formica" kitchen counters. Rub in gently and let sit to bleach out even tea stains. Nothing, and I mean, NOTHING, cleans my SS sinks any better or faster than BKF. It's one of the few things you can use on antique porcelain/pottery/earthenware that doesn't break down the base or glazing.