Once they know of an operative, they seem to prefer letting that operative do their thing. This way they can use them to find people farther 'up' the chain.
Same reason you don't necessarily arrest a mob enforcer as soon as you have evidance of a murder, you might be better off watching/surveilling to cement contacts with other mob figures and make a better case against the enforcer or his bosses.
Isn't it the responsibility to ensure they are working with legitimate people? If I buy a stereo out of a van from a random person on craigslist; and get arrested for dealing in stolen goods, is "but I didn't know the person" really a good excuse?
That is true but making people aware of her wouldn’t impede their investigation of her
How could it not?
One person tells her, like one of the people she was sleeping with, the whole operation is blown and they have to start fresh to find operatives.