Nate had contacted a gentlemen's club and hurriedly subscribed before bringing Scarlet there. She would see how boring it was and never ask to come again.
It was not actually a place forbidden to women - would that make any sense in this day and age? Just, the activities were carefully chosen to appease gentlemen. Most women would find it boring or unattractive.
Sam had gone there for a month or two. She had been attracted by horse riding, but it turned out that horses didn't like her much. All the other activities were so boring that she had interrupted her subscription - to everyone's relief since most guests would be distracted by a blonde woman walking around and complaining about golf most of the time.
Nate was expecting Scarlet to get bored as well. Hopefully, once would be enough.