The courts will kick it back, saying the legislative branch only has the impeachment option per the Constitution. (And they would be correct in doing so.) He knows this is what’s going to happen; when it gets kicked back to him, he will then claim something on the order of, “Well, we’re not happy but it doesn’t rise to the level of impeachment so we’re not going to do anything.” He believes this will defang the conservative demands that he do something.
In other words, he knows this is all for show and it won’t go anywhere.
Maybe so, but it may also be a case of first impression that the Supremes will then need to figger out. We all know impeachment is a bust, so why not sue and see what happens. Better than sitting on hands like the pubes are doing now.