Since 2003, when GHA took over the city's housing stock, Glasgow City Council has forked out around £200,000 a year looking after common ground which did not belong to them.
Some areas of land being looked after by council staff previously housed blocks of flats which have since been demolished.
Now, after a "housing stock transfer legacy review", GHA has been ordered to pick up the tab for its own land.
The proposal was passed as part of the city council's budget earlier this month.
However, Councillor Billy McAllister, is angry the city council has not asked GHA to pay back the money he claims was "wrongly" spent over the past decade.
Today Mr McAllister, deputy leader of the council's SNP group, said: "This money should not have been coming out of Glasgow City Council's budget.
"But even worse, the council isn't going to be getting this money back from GHA.
"Frontline services are facing cuts, so how can the city council afford to give away such a large amount of money, cutting grass that doesn't even belong to them?"
Mr McAllister, councillor for the Canal Ward, is now calling for an investigation.
He said: "I plan to write to the chief executive of the council and demand that we ask for this money back.
"Tax payers' money has been spent on something that it simply should not have been – and we should be getting that money back."
More than 80,000 council houses and flats were transferred in 2003 from the city council to the GHA.
A Glasgow City Council spokesman said: "Stock transfer saw both the council and GHA take on certain responsibilities.
"However, those arrangements were not intended to stay in place forever – and a review has resulted in the proposed future charge, which was agreed by all parties at the council budget-setting meeting last week."
A spokesman for the GHA said: "We're continuing to talk to the council about arrangements for maintaining sites after homes have been demolished."