She was then discussed by the main honours committee in October 2018, as a joint action by 555 wrongly-persecuted post-masters was about to be tried in the High Court.
At least one member of the committee questioned plans to award Ms Vennells a CBE amid growing outrage at the scandal, sources told the Sunday Times.
The Post Office Horizon IT scandal has come under the spotlight following the release of ITV drama Mr Bates vs The Post Office.
More than 700 Post Office branch managers were given criminal convictions after faulty Fujitsu accounting software called Horizon made it appear as though money was missing from their shops.
Despite concerns being raised about Ms Vennells’ honour, Sir Ian Cheshire, who chaired the committee recommending her for a CBE, “brushed them aside”, sources told the paper.
One said Ms Vennells was being rewarded for taking a tough approach to the scandal to keep costs down for the Post Office, including refusing to acknowledge wrongdoing towards postmasters.
“This was her reward for bending her conscience and holding the line,” the source told the Sunday Times.
Another said ministers saw Ms Vennells as “clearing up rather than being the cause” of the scandal she had “inherited”.
The former chief executive, who ran the Post Office while it routinely denied there was a problem with its Horizon IT system, was appointed a CBE in December 2018.
But in a statement on Tuesday, she said she was “truly sorry for the devastation caused to the sub-postmasters and their families” and gave up the honour.
More than 1 million people had signed a petition calling for her to lose the CBE in the wake of the ITV drama.
Questions have also been raised about why she was able to keep a job as a director in the Cabinet Office after her involvement in the scandal was exposed.
A spokeswoman for Ms May told the Sunday Times: “The honours system is an independent process which awards honours to more than 2,000 people each year. Recipients are announced biannually and each recommendation is considered by one of ten honours committees with the final list being agreed by the Main Honours Committee.
“As prime minister, the Rt Hon Theresa May MP, always respected the independence of this system but thinks it is right that Paula Vennells has handed back her CBE.”