What happens if I use Eastwatch-By-The-Sea to move power from a character (Beric for example) to my opponent's House card while he runs the Brotherhood Without Banners Agenda? Does the power get moved back to the character immediately? The Agenda says "When YOU claim or move…" Maybe I shouldn't put so much emphasis on this, but I'd like to ask, since it is not my opponent moving the power, but me, does the power stay on the House?
Thanks.