Love it. It's embarrassing, sure, but it's not lewd. I'm sure that hits the hardest against Nagatoro's defenses. Not that hearing "Tell me your three measurements" or "What kind of underpants are you currently wearing" wouldn't fluster her. A question like that would also give her ammunition with which to tease her beloved senpai, allowing her to recover.
“So what, you wanna know how big my tits are? Hahahahaha.”
“I want to know your first name.”
...
“You know, there’s a such thing as taking a joke too far.”