This one of those grey areas where you may have a by-law that prevents short-term rentals but there is that over-arching clause in Strata Law (referred to by Scotlandx) that prevents the Owners Corp for interfering with the “dealing” of a lot.
So he is right, the answer lies with your local council. Look at the development approval and zoning for your building and make your complaints that way. Short-term rentals are commercial, not residential.
Some councils (like City of Sydney) come down hard on illegal short term rentals, calling them ‘rezoning by stealth’.
By the way, your caretaker is an employee of the Owners Corporation so it can order them to stop handling bookings