Community board member for the Central Ward Michelle Lomax said it's not fair on residents.
"[Those gathering in the square] need to respect the residents' rights as well," she said.
"The continual use of the square in that way and for church services is breaching various bylaws and has caused noise breaches."
Lomax explained the event from a local's perspective.
"It's been really disruptive for the residents because they pull up a truck onto the grass; there's a PA system that's really loud so people sitting in their home enjoying their morning cup of tea have to listen to things [they might not want to hear]."
Charles Drace lives 300 metres from the square and said he can almost make out the words to the speeches from his house.
"You have to give them credit, they are impressive, especially as sometimes these can last for three hours," he said.
Central Ward city councillor Jake McLellan said he has been overwhelmed by messages from local residents concerned about the gatherings on their doorstep.
"To steal a quote from Brian Tamaki 'enough is enough', and the residents have certainly had enough of what has now been months of their peace and enjoyment being ruined."
McLellan, Lomax and fellow Community Board member for the Central Ward Sunita Gautam decided to co-write a letter to Tamaki.
Lomax explained they did it to encourage Tamaki to come and have a sit down with the local community to resolve the issue.
"As the church leader, I thought he could provide leadership to try to help work out a solution that is good for the protesters but also not in the middle of a residential area," she said.
McLellan said there are other places the church can worship.
"There are lots of venues that [Destiny Church] could worship - and absolutely they should be able to worship."
"But if church members are choosing not to ... get vaccinated and they can't access public facilities, then that's on them," he said.
On Tuesday, Christchurch City Council issued the Freedom and Rights coalition with a $14,117 fine, which a spokesperson said covers the costs incurred by the council for protest events before Christmas.
Yesterday, the council also met with Canterbury police to discuss the issue and said it may look at fining the Freedoms and Rights Coalition again for last weekend's protest.
Lomax said while she had received messages from residents about the gatherings, they wanted a mutually beneficial solution.
"The residents are like 'live and let live' but it's just not fair what's been happening.
"I know its really important for the residents that there's a peaceful solution that can be reached. It's not in anyone's interests for this to get escalated."
Charles said that's spot on and no one should be denied the right to protest.
"My objection is a personal objection to what they stand for... I get pissed off by the motorbikes driving around and putting out carbon monoxide.
"There's no way that I can object against protesting since I've been involved in organising so many climate change protests myself!"
- RNZ