Club officials say the group of four, carrying two sets of golf clubs, were seen walking past the clubhouse on Saturday, July 18 before making their way onto the course.
They were later recorded taking divots out of the 4th and 14th greens, with tee markers also found to be missing the following morning.
A car is understood to have picked the boys up at around 10.30pm, with the group leaving the course shortly afterwards.
The incident has prompted concern among members that some youngsters have been roaming the area late at night during the school holidays.
CCTV footage reportedly shows the boys returning to the course later and one of them jabbing a club into the turf.
Club representatives say they intend to review the footage in detail to see if the individuals can be identified.
Green staff were alerted early on Sunday morning and moved quickly to assess the damage to the 4th and 14th greens.
Members helped by replacing divots where possible, but the very dry conditions have made full repairs more difficult.
The club hopes forecast rain over the coming weekend will help the turf recover and make it easier to patch up the worst-affected areas.
Staff say they will continue to monitor the surfaces and carry out further remedial work as required to keep the holes in play
Members have been urged to report any further incidents or suspicious activity on the course, particularly during the school holidays and in the late evening.
The club has also reminded all visitors that the course is private property and that anyone found causing damage will be asked to leave immediately.