Thanks for the answers so far.
These are the exact needles I bought. I purchased them from Hobby Lobby:
I also bought the yarn there but can't get the link to come up. The packaging says it is "Caron Simply Soft" and that it is 100% acrylic.
Hopefully it comes out or at least lightens. It's not an obvious blue that it's being stained, it just looks grungy. I guess I should have noticed it would happen once I saw my fingers were getting stained but I didn't :/.