The authority paid contractors around £57,600 to scrap the "priceless" organ's pipes, which had sat in-situ at the Civic for decades.
The council said it had to pay the going rate to remove the organ's pipes, which it claimed were riddled with asbestos.
However the authority has been criticised by Tettenhall councillor Jane Stevenson, who described the cost of scrapping the organ as "extraordinary".
She said: "It is an absolutely extraordinary amount of money when at a meeting in December I raised the fact that organ societies were offering to take it for nothing. I am not sure Wulfrunians are going to be happy at having had to pay nearly £60,000 to lose something they never wanted to lose."
The saga over the Civic Hall organ has been rumbling on for weeks, with the Express & Star revealing:
Councillor Stevenson added: "Ever since Steve Tovey died the council and John Reynolds have just wanted to find the easiest way to get rid of the organ.
"If the rest of the refurbishment of the Civic Hall had not gone so wrong then I am sure the organ would still be in place."
But Councillor John Reynolds, the cabinet member for city economy at Wolverhampton Council, insists the council had no viable alternative but to scrap the organ due to the renovation cost.
He said: “I share people’s sadness that the organ pipes could not be saved, but there genuinely was no viable alternative. The reality is that the 6,241 pipes, which were not visible and sat behind a wall in an enclosed chamber, were severely contaminated by the extensive presence of potentially deadly asbestos.
“To restore these pipes safely would have cost an extra £2 million that we simply do not have and nor did any other interested parties. For both health and moral reasons, we could not pass on the pipes to anyone else. Legally, the Control of Asbestos Regulations is criminal law and cannot be bypassed by a signed waiver from any person or group, no matter how well intentioned.
“We therefore had to pay the going rate to ensure the pipes were safely removed and sent through a licensed hazardous waste carrier to a contamination landfill facility that has a specific permit to accept asbestos waste.
"The removal of the organ will enable better ventilation for fire safety reasons and adjustments to the stage area to help attract bigger shows to the Civic Halls.
“We have committed £38.1 million to a refurbishment design programme that will ensure the necessary improvements and enhancements are sympathetic to the history of our much-loved art deco, Grade II-listed halls.
“We have worked carefully to preserve the original external and internal features from this iconic 1938 building, including the Compton Organ console, and we are working closely with Historic England, who are supportive of our plans.”