Song cut from movie?

It's a little out of sync, but here's a cute clip of the stars of The big Caper singing on The Jack Benny Program. Mary and Rory say they sang in their recent picture, but this is not the song. I wonder what they did sing. It was cut, but probably was originally intended to show the characters becoming closer. Maybe they sang at the barbecue, but it was felt it slowed down the action. Anyway, here's Jack - http://www.youtube.com/watch?v=oCjmysVxLtA





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