The team's operation led to the recovery of human remains believed to be those of missing tramper Irina Yun.
But the search leader said he did not want the money.
Coroner David Crerar said, in his findings after the inquest into the death of Ms Yun: "I recommend the commissioner of police reimburse the expenses of the search team who located the remains of Irina Yun in November 2009.
Their work was a necessary task to bring finality to this sad event and the location and identification of human remains is an essential function of police and coroner responsibility."
Ms Yun went missing on December 31, 2008, as she was attempting to cross the Cascade Saddle in Mt Aspiring National Park.
She was walking alone from the Mt Aspiring Hut in the West Matukituki Valley to the Dart Hut in the Dart Valley north of Glenorchy.
A long search in adverse weather was called off on January 11, 2009.
Dave Krehic, of Christchurch, had been in the official search, and led a private search party back to the Dart River Gorge in November 2009.
Mr Krehic, a Christchurch auto electrician and member of the Oxford search and rescue team, and his search dog Stig located human bones, which were later identified by a postmortem to be those of Ms Yun.
Yesterday, Mr Krehic told the Otago Daily Times he and his team of three declined payment for the search.
"I really appreciate the coroner's view, but ...
"I do not think it would be right to set a precedent for the taxpayers to pay for private searches.
"I do search and rescue work for the love of it.
"It is my passion.
"After we found Irina Yun's remains, I received a letter from her mother saying our find gave the family closure.
"This letter really touched me.
"As long as my team and my dog Stig gets credit, I am happy," Mr Krehic said.
At the coroner's inquest last month, Mr Crerar said the cause of death was presumed drowning.
