Well, that didn't take long: as we surmised back when the CDC first issued its order halting residential evictions until the end of the year due to COVID (see "How Can? U.S. DHS: National Eviction Moratorium (Roscoe Filburn Could Not Be Reached For Comment)," the order has resulted in a complaint in the U.S. District Court for the Northern District of Georgia that alleges the order is unconstitutional.
No takings claim (not the right court to raise a just comp claim), but there's a lot "there," so to speak: admin law (CDC exceeded its authority), violation of the right of court access, Supremacy Clause, Tenth Amendment, anti-commandeering, this is an invalid exercise of legislative power under Article I.
No takings claim, but read the complaint anyway.
Complaint, Brown v. Azar, No. 1:20-cv-03702 (N.D. Ga. Sep. 8, 2020)