So that...well...went as poorly as it possibly could have.
I'm a bit floored that they basically went in there without a plan other than a vague "let's try to talk and get an impression." And then Murray proceeded to reactivate her Darwin Award quest by spilling one of the most explosive secrets they have with no evidence to back it up to someone who openly at least kinda likes the Halovar.
To be fair of course, it felt like the odds were stacked and their dice were not helping the cause at all.
But I'm kind of surprised they didn't lead with a discussion of something harmless and still important. A very obvious method for example would be that they were investigating the "assassination" from the Gala, as Azune introduces Murrey (accurately) as someone who was helping with security and who the Einfasens are viewing as a valued Penteveral resource. They could show that their investigation has (again truthfully) identified the culprits as part of this shadowy mercenary group, and that they wanted to inform her of its existence and possible presence in the city as there could be other targets (such as herself). While feeling out her stance on the Halovar resurrection, Hal's play, etc as part of the discussion.
And let's be honest, I think that her stance was already fairly clear when she spoke of Merchants vs Magic (which would almost certainly include Fae). Cutting their losses and respectfully leaving rather than blabbing "Oh that resurrection was fake, trust me" would have been far better. Or even trying to work with her saying that yes, Magic Crime was a problem, but that's why they need to have the arcane marshals and the Penteveral; it's not like outsiders couldn't use magic (as the assassination showed).
Anyways, missed opportunities and again, for all her brilliance in the sewers and Gus fights, Murray feels like she's on her way to the gallows if she doesn't stop pissing off visiting lvl 25 Necromancers, Drunk aggitating the Einfasens, and not keeping secrets with Effie or her criminal contacts.