He didn't though. This little myth seems to have grown lately for some reason.
The IOC members see themselves as sporting diplomats who like to be treated like royalty wherever they go. They get to meet every sporting icon alive such as in the Pele, Messi and Ali class. They've seen it all before and having Beckham squash their hand would have just passed them by. He's just a mere sportsman while they are the top sporting administrators.
And he might be a twat, but it was Blair who played all the cards. The amount of lobbying he done even drew complaints from the French as overstepping the mark. Having a smarmy git who was at the top of his worldwide popularity at the time visiting them personally one-to-one is what impressed them. And Jacque Chirac thinking it was beneath him just played more into his hands. Beckham was just part of the team, no more sway than any athlete who was present at the bid.