Having her lucky underwear at his place is nondistinctive. She has to wear it to get the progress; otherwise the lucky underwear is meaningless. But how does she wear it when it is at his place. And if she isn't at his place, but wanna seduce whomever ... how does she get to wear it. It doesn't make any sense bringing it over.
Also the question to solve the endboss in this game of chicken is! Is the first shot for free/500 yen a piece usage underwear a side quest or does it unlock the route to the endboss. And what achievement did he get if he does unlock it?