Danny Fitzsimons of Rochdale is serving a 20-year sentence for murdering Paul McGuigan and Darren Hoare within 36 hours of arriving in Iraq in 2009.
All three were employed by G4S-owned ArmorGroup.
David Taylor-Smith, former chief executive of G4S UK, said the screening process for employees was "inadequate".
The inquest into Paul McGuigan's death at Stockport Coroner's Court has previously heard Fitzsimons was deployed to Iraq without up-to-date references, with no criminal records bureau check and with a forged medical certificate.
He was also on bail for firearms offences in England.
Mr Taylor-Smith said the incident had highlighted inadequate screening of employees and there had been a "systemic failing" in the company's risk management screening process since 2006.
An audit ordered following the killings looked at 527 British employed by the company abroad and found 304 of them failed the screening process.
G4S could not provide criminal records bureau checks for 234, the inquest was told.
Mr Taylor-Smith has since resigned from the company.
During his trial in 2011, Fitzsimons told the Iraqi court he had been suffering from post-traumatic stress at the time of the killings and claimed he had acted in self-defence after a fight broke out.
He had admitted killing Mr McGuigan, originally from Peebles in the Scottish Borders, and Australian Darren Hoare.
Mr McGuigan, a former Royal Marine, had been living in Tameside and had previously worked as a bodyguard for ex-Beatle George Harrison.
The inquest continues.
A security firm which hired a guard who shot dead two colleagues had "systemic failings" in its recruitment process, its former boss has told an inquest.