The union brought up the subject with those in charge of decision-making to get the sitcom pulled from the airlines, reports E Online.
On December 6, Baldwin was kicked off an American Airlines flight after refusing to turn off his iPhone over the application game Words with Friends.
Baldwin later deactivated his Twitter account and appeared on Saturday Night Live to mock the drama.
Baldwin has since apologised to the passengers of American Airlines.
"I guess the fact that this woman, who had decided to make some example of me while everyone else was left undisturbed, did get the better of me," he explained.
Watch Alec Baldwin's Saturday Night Live appearance below (US only):