Danny Fitzsimons was sentenced to at least 20 years in 2011 for killing Scot Paul McGuigan and Australian Darren Hoare in Baghdad in August 2009.
All three were working for UK security firm G4S, which was operating under the name ArmorGroup in the region.
BBC Scotland’s new current affairs series, Scotland 2014, claims to have seen a leaked copy of the internal investigation report carried out by G4S in the wake of the shootings.
It says that in March 2009 - five months before the shootings - G4S carried out two separate audits reviewing the screening policies and practices of G4S Risk Management (RM) - which dealt with armed contracts - against the G4S minimum standards.
The first audit, it is claimed, found the screening procedures for G4S RM only obtained “basic disclosure of criminal records” and “a number of personal files did not include criminal records checks”.
The second audit found that contractors who had worked previously for G4S RM and returned after long periods between assignments had “an absence of vetting” and were “found to be deployed before handing in the necessary information”.
The report states that the G4S RM policies were not consistent with the G4S minimum standards and that “despite ongoing integration plans and significant findings of non-compliance”, the action to move to G4S standards “was not being vigorously pursued”.
It concludes that the feedback from the G4S internal audits “does not appear to have been appropriately circulated or followed up”.
The report also shows the screening and vetting process that Danny Fitzsimons, from Rochdale, Greater Manchester, underwent.
Basic documents such as a completed application form and military references to cover the years he was not working for G4S were missing while details given on his personnel form were “incomplete and inappropriate”.
The programme also claims that the criminal records bureau certificate, which would have flagged up previous convictions, was never obtained and that he was on bail facing other criminal charges.
At the bottom of the compliancy table, where the file should have been signed off, there are two crosses and it states “no check or sign off in place”.
The day after the file should have been signed off, Fitzsimons was deployed to Iraq, the programme says.
Mr McGuigan’s mother Corinne Boyd-Russell, who lives in Innerleithen in the Borders, is calling for answers from G4S.
She told BBC Scotland: “Why would you put guns into the hands of men who hadn’t been vetted properly or screened properly? Why do that?
“It’s not right, you just shouldn’t do that. If they had implemented their processes my son would be alive today. My son would have a life. We would have a life.
“G4S have got a lot to answer for. Although Danny Fitzsimons was the murderer, G4S are responsible for the murder of my son and Darren Hoare. I’ll never ever change that opinion - never.
“It was G4S that put Danny Fitzsimons in that position to be able to murder my son and his colleague. There was a lot of faults made. If those faults hadn’t have been made my son would still be alive today.”
A BBC documentary about 18 months ago claimed that G4S was warned by one of its own staff not to employ Fitzsimons as the staff member felt he was a risk to the public.
An inquest into the shooting of Mr McGuigan, a former Royal Marine from Peebles in the Borders, is due to take place in the autumn.
His family and that of Mr Fitzsimons are calling for a public inquiry.
Liz Fitzsimons, Danny Fitzimons’s stepmother, said: “Compliant with G4S minimum standards? He wasn’t passed on even 50%. It was less than 50%.
“No completed application form, no evidence on file to confirm it was checked, and yet they have repeatedly, repeatedly blamed Danny.
“The sign-off of file... Wasn’t done. So, he never should have gone should he? Never should have gone.”
A G4S spokesman said: “In light of the impending inquest and in the interests of not prejudicing it, we are not commenting.”