Ken:
The term "Stainless Steel" covers a lot of ground, and can mean different things.
The "lesser" stainless is the 400 series, is only marginally "stainless".
The better stainless is the 300 series and it too can rust, if it has not been passivated, or even if it has been passivated and is in the presence of something that will remove the passivation.
If the "rust" is red, or is true rust, there are many different chemicals that can remove the rust, but remember, the surface will not be passivated and will re-rust rapidly.
Classic rust removers which do not activate the surface very much are oxalic acid solutions (5-10%). Hydrochloric Acid will remove the rust stains easily and rapidly, but leave a surface that is highly active, and whereas soldering to it is easy, if you do it rapidly, it will re-rust within a few minutes.
There are many ways to address this problem, but I suspect you want a wipe-on cold answer, which does not activate the surface, and that narrows it down a lot. You can also use Ammonium Bifluoride solutions, but those also activate badly.
The standard passivation (for 300 series Stainless) is to immerse in fairly concentrated Nitric Acid, either for a long period, or hot, or both. This will remove the rust, and leave a nicely passive surface.
Contact me directly if you want more detailed advice.
Rudy Sedlak