Interesting point. In this case, only a minority of Congress and the Senate are behind the petition. It might be different if a resolution were presented and passed by both houses.
In a motion to modify, the argument is that the Court retains continuing jurisdiction to rule in a case where it ruled previously. I think that is how I would plead the jurisdiction.
But does Congress have standing? I guess maybe Congress could apply to be Next Friend for some unborn child. Usually third parties file amicus briefs in an already existing case conveying their position. Surely congress’ legal staff analyzed all this. Wonder if we can get a copy from somewhere of what was filed?