It looks like they have just answered my question on their Facebook page!

Lunch and a water-taxi from GC it is then!

"The Oil Nut Bay Restaurant is now available to outside guests by reservation. Join us for lunch and you will be granted access to our exclusive Beach Club.

The stunning setting, impeccable service and exceptional dining are what make Oil Nut Bay’s Beach Club Restaurant world-class. The main building, adorned with three swimming pools and swim up bar, is just steps away from the pristine white sands of Oil Nut Bay beach. Work up an appetite out on the azure waters with our complimentary watersports equipment or lighthearted beach games before relaxing and indulging in internationally and seasonally inspired cuisine.

Tantalizing and satisfying to the most sophisticated palates, the range of dining choices offers exquisite Caribbean cuisine for lunch, evening, and poolside service. Kids will enjoy the Al Forno oven pizza while adults savor Al fresco light fare.

Contact us to make a reservation for lunch and dinner. Once your reservation is made we will coordinate a water taxi pick-up from Gun Creek."