McConaughey told the Oscar winner he is forever in debt to him because his Toy Story movies are beloved in his home - and his son Levi is a huge fan of cartoon cowboy Woody in the franchise.
McConaughey explains, "His main thing is Toy Story. Toy Story 1, Toy Story 2, Toy Story 3 - 'Papa, I want to watch Woody, where's Woody?' And that's his thing. I mean daily. We have to kind of govern him on it a little bit because it's all the time.
"And so I run into Tom Hanks (on) Oscar evening and I slip him a 100 (dollar bill). And he says 'What's that for?' And I says, 'Trust me, I owe you a lot more than that for the amount of time you've been babysitting my son Levi.'"
McConaughey and his longtime girlfriend Camilla Alves have two children Levi, two, and Vida, one.