In particular, his mother – Mary Maxwell Gates – was on the United Way board along with IBM’s chairman John Opel and reportedly discussed her son’s company with Opel a few weeks before they made the decision to license MS-DOS.
https://www.nytimes.com/1994/06/11/obituaries/mary-gates-64-...
There's little doubt that Ms Gates suggested that IBM look into Bill Gates, but I seriously doubt that IBM made the major business decision to contract with Gates because of his mother's suggestion.