try Barkeepers Friend applied with a moistened Dobie pad
if it's brushed stainless, work in the direction of the brushing.

Interesting... my stainless pots don't do this, so I'm not sure why a tea kettle would. When you boil water, are you turning the gas up too high so that the flames lick the outside of the pot?

I've no other suggestion except the barkeeper's, but I'd try it with a dishcloth first instead of a dobie.

I sometimes get the bluish discoloration on the inside of my calphalon fry pan which is polished stainless ... it looks a bit like oil spots floating on water so I suspect it's from a thin film of cooking oil. The barkeepers friend and the dobie takes it right off and doesn't scratch. I have the contemporary brushed exterior so when I clean the outside, I'm careful to clean in the direction of the brushing.

DH found some stuff called Goddard's Cookware Cleaner in his barn/shop area. We have no idea where we got the stuff, but I used it on a stained area of my SS stove and it worked well. I would try it on a concealed area first, if possible.