According to federal prosecutors, there were a ton of "red flags" that the goods Hobby Lobby brought into the US were less than savory. One expert the company hired to advise them on its acquisitions warned that there was "considerable risk" associated with antiquities likely from Iraq.
US law prohibits the import of objects likely looted from Iraqi institutions or if a "reasonable suspicion" exists that they were snatched; Iraqi law, on the other hand, bans the export of antiquities and has restrictions on just who can own them.
(*Cuneiform is an ancient form of writing on clay tablets that was practiced in Mesopotamia; the seals were engraved dealies that when rolled on wet clay left pictures and cuneiform writing. Both are super important for understanding the culture of the time.)