I bought a very inexpensive special tax stamp lot recently on
ebay with the intent of experimenting with soaking them to try to remove the stains. A fellow collector had suggested to me that it was possible so I wanted to try it out on something I didn't mind destroying should that happen. This is the stamp I selected:

As can be seen from the scan, this stamp is heavily stained with what is most likely smoke. I first soaked it overnight in warm water and some gentle dish soap I use to wash my daughter's bottles. The result wasn't what I had hoped for:

While it did lighten a bit, I was hoping for more. It was suggested I try for longer with a stronger dish soap so I did. The result of the last soaking was better:

As one can see from the last image, the stamp cleaned up tremendously. The only issue is that the red partially washed out and now appears to be orange. I am hoping to try the next one from the lot soon only soak a bit less time to see if I can get most of the staining out without also fading the red.