I looked up how to clean stainless steel cookware so I could maybe squeeze another buck out of the product at our upcoming yard sale. And ya'll, Arm and Hammer does the trick! I've even decided to keep the said kettle. It's so clean I can see my reflection - I guess now I can get rid of a mirror.
I highly recommend you keep some Arm & Hammer on hand - at all times.
(this photo is the real deal and hasn't even been edited!)