Ivy, we all know, is "the Archive."
Luccio explains part of what that means, to Harry; so, the WC knows that much. Probably most signatories to the Accords understand (more or less) about the Archive knowing everything that's written.
But (so far as I can see) "the Archive" is also the supreme commander of the Oblivion War. At the least, she is an integral part of it, and high up in the echelons.
Who knows that information? Very few folks even know the "Oblivion War" even exists. Thomas and Lara, I think, are the ones in the stories Jim has told to date (and Bob, now), but I don't think ANY of them know Ivy's role (I suspect Bob may be able to deduce it). Ivy probably (IMHO) has told Kinkaid: we don't know if she has, but it would make good sense for her primary defender to be best aware of likely opponents. And he doesn't need to actually know the dangerous information -- names, summoning rituals, etc -- to understand the threats & the context.
And I think that's it?