Bud Fox saw Gordon Gekko shred something related to an airline (that's how he got the idea of Blue Star). It wouldn't make sense if it was an airline ticket since Gekko is rich enough to fly his own private jet. So what exactly did he shred?
Been awhile since I saw the film, but I thought in that scene he shredded a birthday card. He said something like "surprise me, it's my birthday", which pushed Bud into revealing the Blue Star information.
I thought the point was that Gekko was so careful about his paper trail, he even shredded birthday cards.
You are probably right, looks more like a birthday card. I find it ironic that somebody will say, "surprise me, it's my birthday" while shredding a birthday card. But Bud already knew it was his birthday and he heard him rambling some inside information issues. So telling him about Blue Star after he saw him shredding the card seems kind of a stretch. An airline brochure instead of a card would've made more sense. Those are my 2 cents.
I don't think it (or the scene) had to do with Bud getting the idea of using his information to trade Bluestar, but pushing him over the threshold so he suggests trading Bluestar even though he knows it's wrong.
In that sense, the shredding of the birthday card contributes: Bud's desperate to get in with Gekko, and he realizes that Gekko cares about nothing except whether this guy can give him a way to make money that a hundred others guys can't.