The minutes of this meeting show that Andrew Wright, the architect on the group, said he did not believe DLE had fulfilled its obligations as cost consultants.
Liberal Democrat MSP Jamie Stone then asked: "Can we fire them?" But Labour MSP John Home Robertson, convener of the progress group, said: "It would be expensive to start again with new consultants at this stage."
The inquiry also heard from George Reid, the Scottish parliament's presiding officer, who apologised for the Holyrood fiasco.
He said: "The engineering and architecture required to turn a work of art into a working legislature has tested all involved to the absolute limit. Design, construction, cost, delay, management, media, human relations and politics have all become inextricably linked. Instead of building a closer relationship with our citizens, Holyrood has alienated them. As presiding officer I apologise for all of this."
Reid was the last witness scheduled for the inquiry, which has sat for 41 days, heard from 66 witnesses and received 20,000 documents.
Reports at the weekend said the main debating chamber of the finished scheme could be used during parliament recesses for the Edinburgh festival and other events.
The corporate body overseeing the scheme said it was considering this possibility.