He said none of the three alternative pools available during the closure - Bay of Plenty Polytechnic, Baywave and Otumoetai - would be suitable, being either too far to travel or too busy.
"It's a nightmare for anyone training for the coming triathlon series - me included - who will have nowhere to swim for a month," Mr Furness said.
"I will have to freeze my membership for a month because I'm not going to be able to swim."
He is angry that, while swimming groups were consulted, independent swimmers such as himself were not.
Nor was he told when he took out an annual membership in May.
After taking a month off swimming, he would have to start training from scratch again, he said.
"You build up your fitness over a period of time. If you have two to three weeks off, essentially you go back to zero. I may as well have just started in October when Memorial opens."
Barry Townsley, 71, has been swimming five times a week at Greerton Pool for the past 19 years.
"We've had no say," he said.
"They've got another pool, Memorial, that opens in October. They could open it a bit earlier to coincide."
Mr Townsley estimated between 20 and 30 independent swimmers used the pool between 6am and 9am.
"They haven't asked us guys who swim all the time."
He would be swimming at the polytech pool during the closure, which would cost him $5 a swim, compared to the 80c he pays through his annual membership at Greerton.
He would suspend his Greerton membership during that time.
"I know the swimming clubs are probably there a fair bit, but so are the public. They pay a fair bit towards the pool."
Tauranga City Aquatics chief executive Tania Delahunty said the main user groups, which included swimming squads and a swim school, had been consulted because they accounted for the bulk of users.
With 120,000 user visits a year, consulting all users was "physically unworkable", she said.
The dates chosen spanned the school holidays and best fitted with the national swimming programme, she added.
"If they are out of the water late in the year, it impacts on their year-end swim meets."
Greerton Pool members would be able to use their membership at Otumoetai and Baywave during the closure at no extra cost.
"We think that is fairly fair and reasonable. Every pool has to close for maintenance," she said.
Timing the closure to coincide with the opening of Memorial Pool would not alleviate the problem, as Memorial was already fully booked, she said.
"We don't have a pool that's sitting empty. We have to manage the pools in the best way we can. It's a big balancing act."
During the closure, both pools will be painted and the changing rooms refurbished. Work will also be carried out on the plant.