If he feels really strongly about this he could pay the Grand High Priestess to evaluate Carissa's competence probably that's a bad idea, for many reasons but among them that Carissa doesn't actually know what the Grand High Priestess would truthfully say.
What is the meaning of an oath is a hard question for us to answer, with our vocabulary, but it doesn't mean that oaths only mean to us their most obvious physical consequence, and many people who one way or another don't fear Abaddon still give their word and mean it, groping for a different basis for it to signify what it does.
There's really something to be said for doing things and checking whether they have good or bad consequences, assuming the consequences are recoverable.
Also he could just directly bring this to Carissa, she'll in fact probably be upset and definitely at least somewhat turned-off but that's only a consideration against it, not absolute reason if he's too stuck.