It just happened that George had enough time to offer Winter an invitation before Marcellus and Ace appeared in the scene.
Contrary to what he seemed to be claiming, she could handle the situation well enough. She may not be able to manage or control people like what he said, but in the first place, there really was no need for such a thing. Though she does want something from her targets, she already learned her lesson from that one with Violet -
Winter thinks that she shouldn't treat them as mere objects of interest.
They have feelings and circumstances too, and they deserve to have a kind of relationship that isn't limited to their line of work. That said, she hopes to have something more to her connection with them. She knows that the world they live in is different from hers, but she at least wants to understand them in a deeper sense.