Not that it matters too much in the current situation, but Lady V did correctly identify whose daughter Katharina is.

Katharina did not leave home on the best terms, though … but he might still be willing to pay something for her safety.

↓ Transcript
Shara: Wow ... you're REALLY SELLING IT, straw ...
Straw: Hey, when have I not been honest with you? Look, those Black Fist guys are probably gonna keep you. And as far as I understand you're not exactly FRIENDS.
Straw: But you're a SURVIVOR, eh? If you get through the next weeks without loosing too many more limbs ... who knows? You might get a chance to FUCK OFF somewhere. That's the best I can do for you at this point.
Shara: A-and ... Kat ... ? ... what do they want with HER?
Straw: Oh don't worry about your FRIEND. Lady V just wants to sell her back to her DADDY or something like that. She'll be fine.
Straw: Well ... unless the Black Fist pays MORE for her. I kinda wonder wether YOU or HER are gonna have a worse time with them ...
Gideon: <in Shara's head> Soon. Be ready.
Straw: Sooo ... looks like you FINALLY gave up? Good thinking. And don't worry: We'll have your friend soon enough.
Gideon: <in Shara's head> Don't move.
Shara: <thinking> ... why?
Gideon: <in Shara's head> ... your little white boy needs a clear shot.