Here is a link to the "Contact Us" page of the official MCO website. You can use the Feedback Form or click on the Contacts tab to get a phone number or mailing address:
http://orlandoairports.net/contact/contacts.htm
In all honesty, I doubt you'll get far. The area of the website that shows The Club says that it is "Accessible only by passengers departing from Gates 70-129".
Also, under "Getting Around" section of the Frequently Asked Questions page, it does explain how to do what you wanted. However, it also includes this sentence: "Please note that this may not be possible during certain times of the day for security reasons while international passengers are arriving in the terminal."
FAQs page:
http://www.orlandoairports.net/faq.htm
Obviously, most people aren't going to visit the official airport website. I think a sign is probably a decent suggestion. That said, maybe there is one and you just missed it.
You also may want to contact The Club at MCO. I'm guessing that they might be more responsive than the Greater Orlando Aviation Authority (the government agency that runs the airport). Perhaps The Club could inform guests about this issue when they arrive.