The Constitution prevents any (uninvited) god that's not the Overseer from entering:
With the exception of the Overseer, the gods of Olympus, their associates, Lady Hestia and Lord Hades are hereby forbidden from entering the Labyrinth without express invitation from the Master of the Realm.
Only if Clement (or a previous master) invited Athena in would it work, and I thought the woman Clement met was already in the Hotel... Heck, I think Athena would've been pretty unhappy with Asterion being locked up and not 'actually tortured' again, too, she would've rather wound Clement around her finger to return to the old ways.
Though I will say, in the Ruthless route we do learn about the 3 other 'minor' gods who are involved in our story and contributed their blood to the creation of the Realm, because one of them outright shows up. How did the realm allow them in if the Constitution should've kept them out? Even if they aren't the main 12 gods/Hades/Hestia, they're still a god of Olympus, no? Maybe they never left the realm in the first place? I don't think Nemesis or her sisters would be banished to the Realm for any reason, but that's another way in maybe.