OT: There were plenty of real prostitutes back then and now, for high and low class. The profession (which they were sold or bought) didn't involve sex per se, but you can imagine that since quite a lot of them get married after their career (or end their career when getting pregnant), there was some voluntary copulating going on
. As far as I've understood, this has been more like 'after work' and didn't involve money at all.
Also I wouldn't instantly call all the girls in that profession prostitutes if some patron would offer huge amount of money for some after-hours fun, more likely they put this money to their own pockets and the tea house had no idea about it.