I dunno if Jack would mention this to Jayden or not BUT they do technically know each other so I'm throwing this in here anyway. Jayden wouldn't do anything to try and stop Jack from getting the Mysterious Acolyte out, though he also won't necessarily think this is a good plan; he'll bring up the idea that it's entirely possible she's a plant no pun intended and that taking her with them might be really dangerous. But since that's only a suspicion with no evidence he's not about to actually say she should be left behind, though he isn't going to actively help either.