I think we'll see some connection that the girl was one of the younglings shown in the temple. She probably saw the holovid of Anakin and Palpatine that Obi Wan and Yoda saw Obi Wan probably told her to hide basically the same thing he told the jedi who was killed on Tatooine. She did and was miserable and was captured by the inquisitors before joining them and she views Obi Wan as betraying her.
Or it's just known in the Inquisitors which isn't out of the realm of possibility. The people who answer directly to Vader probably want to know as much about him as possible to hopefully supplant him and become a Sith Lord, I'm sure that's the goal.
My gripe was her seemingly killing the Grand INquisitor, but we'll see how this plays out. She may not have killed him, or the one we know from Rebels just hasn't shown yet, but I consider that unlikely as Fifth Brother looks a lot like the same fro mRebels. As does the GRand Inquisitor. But maybe now we'll get a Jason Isaacs Grand Inquisitor that we deserve.
I have a feeling he's not dead but we'll see.