The records have been demanded due to allegations that Co-operative Group's bid for the 632 branches in the Verde portfolio was favoured by Government ministers until it collapsed last year and it was revealed Co-op Bank had a £1.5 billion capital hole.
Mr Tyrie had asked for records of contacts between Treasury ministers and officials with Co-op, Lloyds, failed bidder NBNK and UK Financial Investments, which manages the taxpayer's stake in Lloyds.
He told Mr Osborne that he had provided "some general information" but his response "lacked the detail required" such as timings of calls, those involved and the content of discussions. Mr Tyrie demanded this be handed over.
Co-op has continued to be hit by the fall-out from its collapsed Verde bid. It confirmed yesterday that former Labour Cabinet minister Lord Myners, who had been tasked with recommending reforms to the way Co-op is run, is to leave its board at its annual meeting in May.
There have been reports that he is stepping down due to concerns about opposition from other directors to his plans.
Lord Myners said: "I am pleased that I am going to be able to complete my governance review and that the outcome of that work will be presented to members at the general meeting.
"I am confident that there is a good future for the Co-operative Group if it commits to doing the right things on governance and leadership."
The departure of Lord Myners follows that of chief executive Euan Sutherland, a Scot who previously ran do-it-yourself chain B&Q, who quit from what he described as an "ungovernable" organisation after only 10 months in the role.
Co-op is owned by its 7.2 million members, including 475,000 in Scotland where it has around 400 food stores.
A reconstruction of the Co-op Bank led to it ceding majority control to a group of hedge funds. The state of Co-op Bank's finances will be revealed in results published today.
Co-op Group's full-year results are due to be published next week. They are expected to show a loss of around £2 billion.
Co-op's problems have been exacerbated by the arrest of former bank chairman Paul Flowers as part of an investigation into the supply of illegal drugs. Both Rev Flowers and NBNK chairman Lord Levene have claimed there was political backing for Co-op.