At its first face-to-face meeting in over two years, Councillor Brian White asked that the rule be reconsidered since members of the public attending in the gallery, and staff, were not required to do the same.
"At the county we have rescinded that requirement as well for council, so to the member of the public who raised this issue with me, I appreciate that you raised this inconsistency," he said.
Councillor's Margaret Bird, Mike Stark and Terry Burrell attended Monday's meeting virtually.
Councillors Stark and Burrell voted against the motion.
Mayor Mike Bradley had planned on attending virtually, but ended up chairing the meeting from council chambers due to technical difficulties with the hybrid format.