I recently got my foil Japanese Dark Depths signed by the artist, but unfortunately the ink didn't dry, and when he put it back in the sleeve it smudged the ink all the way up the card!!!! Does someone here know of a solvent you can use to remove the ink and not damage the card? I used a gold ink pen (not a sharpie) and it can be scratched off, but it still leaves a little residue on the card that is noticeable. Please help! The card is insane hard to find and quite expensive, and was pretty much ruined by the signature

Perhaps nail polish remover in a very small quantity? Don't use pure acetone; that's what people use to "blank" (remove the face of) foil cards. It also might be worth buying a similar pen (unless you have the pen already), writing on a few foil commons, and testing first.

Unfortunately I borrowed the pen and I don't know what brand it is so I can't replicate it. I guess I will use a sharpie on a random foil, and try using the nail polish you mentioned. I was hoping someone knew of a surefire way to fix this, but hopefully this works.

If you haven't done it already, get some of the "eco-friendly" nail plish remover. The less it stinks when you open the bottle the better it will be. You have to really rub that stuff in to start getting the regular card foil & ink off so it should be much better than the cheap stuff.

Invest in a wife/GF who already has this stuff and it's even cheaper!

Acetone will take it off, and SHOULDN'T damage the foil.
But what you want to do is sign another Coldsnap foil (japanese shouldn't matter) with that pen, smudge it similarly, and try it.
I say coldsnap foil, because the foiling process has changed a lot over the years, and foils during certain times were way more susceptible to acetone removing the print.

I don't advocate nail polish remover.
Nail polish remover is acetone, but it is acetone with water in it, so it can damage cards more easily.

I've had some success removing sharpie from cards using a wetted toothpick. The card was old and the sharpie ended up staining the unvarnished cardboard, but it was enough that I could sleeve it up without it showing through (someone proxied Visara the Dreadful on the back of a personal tutor!). With a new foil I can only guess the outcome.