The press release is here. The theory is a major equal protection stretch: it is that it violates the rights of Wisconsin voters who did not sign the Walker recall petition for the government not to affirmatively check recall petitions for duplicates. (The GAB’s position is that it is up to those challenging the recall petitions to complain about duplicate signatures.)
Though the complaint does not cite any caselaw supporting the equal protection theory, I suspect that if this goes further the Republicans will rely on Bush v. Gore. Indeed, my impression in conduct research for The Voting Wars is that Republicans have relied upon the equal protection arguments in Bush v. Gore more often than Democrats in the last decade.