rhynne,
I do not know of any way to remove the rust stains from the paper.
However rusted staples can be replaced. Most modules use standard staples. Just like the ones in your stapler. Get some tweezers and gently lift the curled ends of the rusted staples upright. Most of the time they break right off - which is no problem at all. Remove only one staple at a time. Once you have one staple removed replace it immediately. It is much easier when the other staple is left in to hold the pages together. Use the back end of the tweezers to curl the new staple tines into place. Repeat for the other staple(s).
Ideally you want to replace staples when they just begin to show rust. That way you avoid the stains. I have been very successful in replacing staple on most modules. Some
Mod series use different sized staples (Islandian Games) just check the size before starting.
Martin