Actually, it is used as an answer to thanks: Дякую - Прошу ("You are welcome")
Oh, I've thought he means a way of saying 'please' (after all, the original sentence had «будь ласка»).
I grew up using "прошу" instead of "будь-ласка" . . . it could be a regional use that my grandparents were used to, plus a lot of Diaspora Ukrainians used it here in this part of the USA when I was a kid.
Both are pretty widespread, I believe.