Nothing, which is evidence against naive Conspiracy, because naive Conspiracy sets Carissa up to ask that only if they've got some startling revelation planned. Competent Conspiracy knows how Keltham will access it. You would think the Conspiracy would be competent by now, they've got Carissa and Asmodia now even if they didn't have them before.
"Not... actually the kind of suspicion I had in mind, though I guess it could help on having context for where this came from. More like, there's some other reason you had to get me out of my bedroom, couldn't tell me why, 'Rovagug cultists' are the excuse because that's what squares with the story about how this place is protected from gods..."