Can you imagine the clerks at Thomas' office? "Fer cripe's sake, why us?"
Actually, she did do this right. In an Application for Emergency Stay/Injunction, the case goes to the Justice assigned to cases for that Federal Circuit. Justice Thomas is assigned the 11th Circuit. It isn’t a petition for Certiorari. IIRC, if he denies (as I suspect he will), she can go to any other Justice she chooses.