Exploit how? They have no leverage over us, nothing to threaten us with, and they can only use "she's totally our agent" lie on others until we learn about it.
Easily, and as part of a balanced breakfast of influence games. Lara's even doing it right now.
We were the ace card she played to win the consolation purge, continued to us is part of how she's proceeding with that. Which gives us power over her but is also a tie itself for Lara to play with.
Marcone did a lot of different things to get where he ended up in canon, but one of his first big breaks was convincing people Harry worked for him in some capacity. It got people to hesitate, to think he was more involved than he was, and to give him space to find his bearings.
The consequences of Dresden not opposing this were that even in the face of firm denial and significantly more relevant connections people still thought he at least was a hired killer for some muggle asshole in the past if he wasn't still on the take right now.
Lara doesn't need the same things, but she explicitly is pulling the same trick right now. Why would she stop?
The more she does that the more people will self select their interactions with us based on what she's saying instead of what we're actually like before we even get a chance to do anything.
That's just one game too, there will be more because that's how they do business.
You're making a similar mistake to those who underestimate social combat because it doesn't involve explosions. This is social combat over time and large groups, we just can't see the proverbial dice pools because we're basically sleeping through the fight.
Not that we're in critical danger right now, but this sort of issue sneaks up on you. If you wait until things are obviously a problem fixing them is much harder where it's possible at all.
Lydia is a child, but she's still Background: Mentor 1 Arawn
He's dead right now, is she speaking to anyone on his behalf?
Again, this is all about who is talking and what they're saying.
A silent death god isn't worth a dozen whamp barons flapping their gums even if he could shut them down with a word.
We need to be talking in addition to doing if we want this to work out.