What was the FBI hoping for by recruiting her as an informant anyways. They ought to know that bosses like Tony Soprano don’t sit down with the girlfriends of their men and give them the details of whatever crimes they’ve committed.
They were hoping she would give up Christafuh, and then he in turn would give up Tony.
They were looking for any way in. So they were hoping to use her to flip Cristofuh or pick up any other intel they could get. They already tried it with big Puss and he got whacked. They planted a bug in a lamp at Tony's and that didn't work. They were willing to try anything.