The letter from the convener Linda Fabiani to John Swinney comes after the deputy first minister confirmed to the committee that no minutes were held of key meetings with counsel in November.
The committee said that it was “extremely frustrated” that evidence sought by the committee for months was being “sourced and published in the final days of this inquiry”.
The body said questions would have been asked of senior civil servants, the First Minister and the Lord Advocate had the information been made available earlier.
Members also expressed their disbelief at the suggestion no notes from meetings involving counsel were taken.
The letter states: “The committee is concerned that Scottish Government officials, such as the instructing solicitor, were not required to produce notes of meetings with counsel including of decisions taken.
"In addition to the need for transparency to enable scrutiny, the committee does not understand how in the interests of good governance, the Scottish Government would not create and keep records of such crucial meetings.”
The letter also asks for “assurances” that phone consultations between counsel and the Scottish Government is included in timelines and whether counsel have been asked to provide notes or minutes from key meetings.
It comes as Mr Swinney faces a no confidence vote in Holyrood on Wednesday that he is likely to survive due to backing from the Greens.
The committee letter also follows reports of an additional witness backing up the claim Geoff Aberdein, Mr Salmond's former chief of staff, was leaked the name of a complainant in March 2018.
Alex Salmond’s solicitors Levy and McRae may be separately served with a section 23 notice by the Holyrood inquiry examining the botched handling of harassment complaints against him.
It is understood the prospect of a third use of the previously unused powers of Scottish parliamentary committees is still being actively discussed by the committee.
Issuing the notice would follow the suggestion to do so from Mr Salmond himself, who told the committee his solicitors were “extremely willing” to pass on information.
Included in this would be information disclosed to Levy and McRae by the Crown Office and the Scottish Government during both the judicial review and the criminal trial.
Mr Salmond alleges there is information supplied to his lawyers during the trial that would shine a light on the “malicious plan” he claims was concocted to remove him from public life.
He suggested a section 23 notice would allow for his legal team to pass on this evidence without falling foul of section 162 of the Criminal Justice and Licensing (Scotland) Act 2010.
The former first minister has said the Crown Office repeatedly threatened him with prosecution under this section, which forbids the use of information disclosed during a criminal trial for any other purpose.
The committee is examining the botched handling of harassment complaints against Mr Salmond by the Scottish Government, which led to a £500,000 legal bill after the Government conceded a judicial review challenge on grounds the process was “tainted by apparent bias”.
Mr Salmond was also acquitted of sexual offence charges in a trial last year.