My wife's Lady Gillette had a rusty blade in it and the rust moved to the head of the razor. How should I go about removing the rust?
The same thing happened to me with my gold colored Gem featherweight. I had gotten ahold of bad blades, and just left them in the razor as though it was any DE blade... I even used it a second time before I noticed rust everywhere . The blade had rusted to the thing and I had to pry it off. a CLR soak and deep scrub got it off, but there was still a little area where you could tell it had been... So I put some elbow grease into it and managed to rub it off with my fingers... Thankfully, its back to normal now, gold color and all
Don't use CLR on that Lady Gillette - the handle is anodized and CLR is WAY too harsh.
As Darjeeling Express said, scrubbing bubbles is all you need, along with a toothbrush for the worst rust. If you can't get the bubbles I have found the Comet Bathroom cleaner liquid (NOT Comet Powder!!!!)
works fabulously.
Looks like this;
FWIW, I have cleaned two lady gillettes using CLR with no problem. YMMV.