What happens to my claim during a power challenge if I play with the Brotherhood agenda and have no Brotherhood character in play?

Does the power leave my opponent's house card?

Does it just get discarded or do I now have to move it to my house card since I can't move it to a character! Or does the power remain on his house card?

I don't think you will be moving it from your opponent's house card because theres no place it can go.

The claim effects for a power challenge are to move power from card A to card B. With the Brotherhood Agenda, "card B" must have the Brotherhood trait. If you do not have a Brotherhood character, you cannot complete the claim effects, so they don't happen. You don't get to move it to another card, and you don't get to resolve it "half way" by taking it away from your opponent.

If you are playing the Agenda and you have no Brotherhood characters, the claim effect for winning a power challenge never happens.

It would be like winning a military challenge against an opponent with no characters, or an intrigue challenge against an opponent with no cards in hand.