Oh... Shit. Yeah, she's the Caretaker alright and, based on Jack's fear, she has a reputation of doing whatever it takes to keep the experiment balanced.
What can she do? I've got a mental image of Ardent standing in front of a pit he just dug in the woods, Alice standing behind him with a gun pointed at his head. She's about to 'take care of it', as Jack so nervously put it. I doubt it will go that far but I think she has a lot of power and resources and the freedom to use them to protect these people.
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Of course, if she uses the 'headology' tactic, she could be very, very subtle. Maybe up to and including an entirely psychosomatic 'curse' that is a negative reinforcement against what he thinks he wants ("All hominids on this planet are non-symptomatic carriers of a permanently-disfiguring STD. The only way to escape it is to never enter this planet's ecosphere again."). Basically, not only make him leave and be afraid to ever come back but to also make sure everyone he contacts is afraid to ever visit.