"Well, he tried to straight up shank me, but yeah, other than that, we're totally cool."

If you're wondering why Selina isn't ratting out Desolair to the king, it's because even though she probably should, she sees this as letting him off the hook, and hopefully as a way to potentially gain his trust. Is it a bad idea? Most likely. But Selina goes out of her way to avoid conflict, and wants to get along with everyone.