T206 cleaning/soaking advice...

[Bridwell]

I don't think this type of soot and other discoloration will soak off or clean off. I predict you will be disappointed if you try it.

[Leon]

I will echo the others on it. Those don't look like stains that are going to come off. Could be mildew...
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[SyrNy1960]

Not sure if anyone has ever used this stuff, but it works great. It won't damage your card (well, I never had it happen. Always used a cheap stained card first to test it). I purchased many cards (50's, 60's and 70's) with stains, soaked them (individually) in a sealed-tight container for a bit, then once you open the container, you will see the liquid quickly evaporate on the card. Didn't always work (depending on what the stain is), but it most cases it did work.

[Snowman]

Are we sure this is ink on the back? It looks more like mildew or black mold to me. If so, that's not going to come out with water. You'd probably have to use some harsh chemicals to get that out, and that would likely ruin the card.