I get a similar discoloration/buildup in my kettle, around the welded fittings and on the bottom, where the kettle rests on the burner.
Basically - I get stuck-on deposits (and perhaps a bit of rust) where the stainless is not completely smooth (like the weld line on your IC tubes).
I wash with PBW after every brew to remove trub, hop matter, etc. Every once in awhile, I'll also run a wash of Barkeeper's Friend (primarily Oxalic Acid) to keep the surface shiny and free of deposits/discoloration.
A quick soak in Barkeeper's Friend, coupled with a little elbow grease, should take care of it.
NOTE: make sure to use the Bleach-Free Barkeeper's Friend