Bethe wasn't too happy as he was the junior and Gamow was pretty senior and unrelated, so Bethe didn't get the credit he deserved iirc.
Bethe went along with the joke when Gamow added his name to the paper. But the actual loser in the deal was Alpher because most scientists, upon reading the author's names simply assumed that Bethe and Gamow had come up with the main ideas.