I see this as a catch-22. Damned if we tell, damned if we don't. It's only a question of degree if damage.
If we tell nothing now and it comes to light later, if will lose a lot more trust and put everything in the meantime, and even before, into question. Who's to say this was the first meeting with a demon, after all.
If we disclose our meeting or even our apparent candidacy, it will be a hit to our rep, yes, and will lead to some more scrutiny in the best future. We can deal with that. But it isn't a lever in enemy hands anymore, ready to unseat us at the worst moment. And guess what? Algard and Starke know the mind games. If we tell them, they'll know how to deal with the information, and can prepare for when the enemy tries to use it. That's half of Starke's job. Recall our meeting with him over our failure to turn the Wurtbad watch to Ranald. Crippling us over this would just play into enemy hands, and they know that at least as well as we do.
So bite the bullet and trust our boss and comrades to know their jobs.
[X] [BELEGAR] Daemon and weakening
[X] [COLLEGE] Everchosen, Daemon, and Mathilde's candidacy