Earlier this year, the Kingston Gardens Neighbourhood Watch Group sought approval from North East Lincolnshire Council to build a 3ft high fence at the Grimsby beauty spot.
But after the £400 wooden fence went up in May, the council complained that it was blocking access for its maintenance vehicles.
"The council said they misunderstood us and thought the fence would be put in on the other side", said the group's chairman Alec Leonard.
"It was a misunderstanding and they have apologised profusely for that."
The fence was erected along the boundary between the wood and the green – running diagonally between Kingston Avenue and Littlefield Lane – to prevent motorbikes and other vehicles getting into the wood and churning up the soft muddy ground. However, council bosses thought the new fence was going to replace the existing pole and concrete fence, which runs parallel to Kingston Avenue.
It now wants a section of the fence removed to create an access for its tractor, but the neighbourhood watch group is standing firm.
It has suggested creating an alternative access point to the wood further south down Littlefield Lane, where the ground is harder, by removing three wooden bollards.
Mr Leonard added: "They are saying they need access for their vehicles. We are saying they can have a better access. We are hoping to persuade them to take the common sense option."
A spokesman for NELC said: "We do appreciate the work and effort carried out by the neighbourhood watch group in relation to Kingston Gardens; their keenness to maintain the site as an attractive natural haven is to be commended.
"However, with regard to the fence which has been erected, it does restrict access to the gardens and the woodland, preventing pedestrians and maintenance vehicles from getting onto the site.
"Therefore the council is now considering what it can do to reinstate access, and it is hoped that a decision will be made on this soon."