We know that Carey was the GTVA mole that gave the UEF the Agincourt's jump schedule, but there's another mole in WiH: the person who gave Steele the information about the UEF - Vasudan meeting.
Are you really so sure it was Carey herself who gave away the information.
I always assumed that, when Carey gave the UEF informatinon, she did so in a way that didn't give away her identity (I certainly wouldn't want to broadcast my identity to someone I'm not 100% sure I can trust over a transmission that might be intercepted), not even to the UEF. And thus, after she was discovered and caught, the GTVA could just send someone acting the same way Carey did, but giving out misinformation, without the UEF ever noticing the difference untill it's too late.
I know Careys interrogation hints at the GTVA doing brainwashing, but considering how little time passed between Carey giving the real information and the mole giving out the bait, I think Carey still being in the brainwash camp and someone else contacting the UEF through her channels is more likely than her being turned so quickly and completely.