Well I already unlinked it once but I couldn't submit it to the new recording (I have the mp3). After I press scan in Picard the song just stays on the left pane and it won't work even after the AcoustID tag is filled and I press lookup. So I just linked it again to the old recording so at least it will still get a match (albeit incorrect one). But having the ability to just move the AcoustID (or just link it to another recording if it was unlinked from all of the other ones) would be ideal.
As for why I can't submit it to another recording, I guess it has to be a new AcoustID fingerprint which does not exist in the database in order for you to submit it. And because in this case it exists already(just not linked to any recording), it will not allow you to submit it.