Huh. I didn't know they could still do that, having already heard oral arguments in the case.
In theory, each justice would need to state credible grounds for recusal. In practice, since nobody can contradict the Supreme Court (short of the impeachment of a Justice by Congress, which is never going to happen in this climate), any justice can recuse himself/herself from a case at any point for any reason or no reason at all.
It would be a "break glass in case of emergency" kind of maneuver, but in this case, overturning Roe v. Wade would be so shocking that it just might be what the doctor ordered.