Think of it this way:
Realistically the gendered introduction thing is a subculture thing. Yes, it will likely confuse Lesley unless she's been around thise who use it, or if she knows of it could signal a degree of compatibility or incompatibility based on her views because Leslie, by using it, has announced he has some strings somewhere attached to this subculture (he's probably not trans, so he may have a sibling or close friend who is LGBT, which is a very possible, fairly likely to happen real world scenario).
So, why isn't she just getting over it? Yeah, it probably seems weird to her, but that doesn't make it wrong that he's asking. It's just something that's new to her and it does her no harm to realize what it is and accept it for what it is, and if she doesn't like him she can end it and likely well forget about the whole thing by the time she ends up hearing it again.