The hut is one of three the five family members of the Mt Ida Syndicate say they own, as part of the 113-year Mt Ida grazing or occupation licence.
Land Information New Zealand (Linz) decided in 2008 to cancel thre licence, but that decision is the subject of an appeal.
Syndicate member Jock Scott said while visiting the hut last November to prepare for a straggle muster of sheep, he found Doc staff removing a coal oven from the hut and replacing it with a log burner, and also using a small digger to build a toilet and to remove some debris from around the remote hut.
"We were never contacted that this was going to happen," he said.
In 2003 the Commissioner of Crown Lands advised the Mt Ida Syndicate and Soldiers Syndicate grazing licences would be ended and the land would be managed by Doc, as part of the Otiake Conservation Park.
The Soldiers Syndicate last year successfully appealed in the High Court in Dunedin, claiming that the commissioner had reneged on an earlier decision to allow continued grazing.
The Mt Ida Syndicate has also applied for a judicial review.
A date for a High Court hearing has still to be set.
Syndicate lawyer Kit Mouat said that appeal was filed on June 11 last year and Doc should not have removed any items until the result of the hearing was known.
If the review went against the syndicate, they were entitled to compensation for any improvements, he said.
Mr Scott said the five syndicate families owned the chattels and improvements on the 8500ha run block, but removing the coal range had wider implications for the group of friends and families who each summer take sheep out for grazing before returning in April for the autmumn muster.
Last month Mr Scott said 16 people helped him on the three-day drive to take sheep to the mountain for the summer, coming along for the experience and for the tradition.
Cooking them a roast on the coal range was a lot less onerous and demanding than using the camp stove they had to bring in with them, he said.
"It's just not practical."
Mr Scott said the five syndicate families owned the three huts: Tailings Creek hut, the Boundary hut, which was the former Ida Valley railway station, moved there in 1974-75, and the Wire Yards hut.
Another hut, at Chimney Gully, was historic and was kept as a shelter for musterers.
Mr Scott said they also owned the fences, but their landlord, Linz, was disputing whether the syndicate owned the the tracks.
Fellow syndicate member Laurie Inder said common sense should show they did.
"They [Linz] wouldn't have got there without our tracks."
Access to the grazing blocks for the families' 9000 ewes was vital to the sustainability of their farms on the Maniototo Plains, where Mr Scott said summer drought would make most members' farms uneconomic.
Mr Inder said the high quality of vegetation and soil on Mt Ida, as acknowledged by Linz and Government contractors, was a testament to the syndicate's management.