Certainly, they know there's someone behind her, so for their own sake, not even for Grete's sake, they are better off capturing her alive and trying to find out the identity of the one lurking in the shadows. Especially since she's not quite herself, interrogating her ought to be effective. Though they still need to be careful because the one programming her might have left behind false information she would reveal more easily than the identity of the real culprit.