I got back a PinkFresh stamp set today that a crop buddy borrrowed. It's been really badly stained and I've tried everything to clean it. I think she used chalk ink? It's a message stamp so not being able to see through it to line it up properly is going to be a problem. Would love any suggestions of what to try next.... beyond replacing it!
You might try rubbing with a microfiber cloth to see if it budges anything. Probably won't work if it's truly a stain though. It's one of my go to cleaning supplies around the house but I haven't tried it on stamps. The other would be a Magic Eraser. I would only use that if I was ready to toss the stamp if I couldn't clean it though. The abrasive might backfire badly. But they are magical for cleaning other stuff so it might be worth a last ditch try.