And if the funding goes away….so does the school. It’s probably on parish property.
So, yeah…good for the Bishop.
What the school may be hanging it's hat on, however, is the claim to be "under the Jesuit tradition." If it is a Jesuit financed and run school, he can probably legally forbid them from calling themselves "Catholic" in his diocese, but the Jesuits have control over administration and probably at least some of the financing. This is why, for example, the Jesuit-run University of Notre Dame in Indiana gets away with the shenanigans they do.