She says, explicitly, right there on the page, "I know Oracle doesn't approve of me."
This is a blatant falsehood. Babs does approve of her. Babs likes her. She likes Babs. They both know this. And she's absolutely playing up the outsider thing, her whole internal monologue is whining about how the Bats give everybody second chances (except her), precisely the way she used to whine back before, you know, Babs gave her a second chance and she warmed up to the idea and started extracting promises from people to behave instead of dropping them off buildings. There's no "annoyed" here, there's angry petulant martyrdom oozing off every word that she's incapable of shutting up about for even a second.
If she were really just "can't tell you how much I love that no kill policy," she'd just... say exactly that. To Barbara's face (or at least the over-the-comm equivalent). And then get on with the takedown. Instead of whining nonstop for twenty pages about how dangerous he is (when he clearly really isn't, she's not having any actual trouble keeping him from hurting anyone other than her), and then actually trying to kill him at the end for no other reason other than she apparently gets sick of whining.