Despite knowing that Edward is aware, Rex doesn't care.
He has other things in mind.
It would be a lie if he said that what Mavenna said to him didn't trouble his mind, he became more worried about Gistella. He feared that she might get corrupted by the Executor like Edward did which would be very troublesome.
Knowing that the Executor was acknowledged as a rival by the System, he was paranoid.
Rex feared that the Executor might have a way to do that.
Moreover, the real problem would come this night, when the actual Hare Moon appeared.
Even though he was confident in his ability to withstand the Hare Moon's influence, believing that he was stronger now and would definitely have an easier time resisting the Full Moon, all such notions had been mercilessly erased from his mind.
Last night made it clear that he couldn't do anything against the Hare Moon's influence.
Staying here until the Hare Moon comes will be detrimental.