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The TSA has no legal right to organize, but negotiations were opened with the AFGE to represent TSA screeners in June 2021. The agreement was signed in March 2024.
As an aside, on social media, you routinely read comments to the effect that federal employee unions were created in 1962 by John F. Kennedy's Executive Order 10988, and all that is needed to abolish them is to repeal that order. That is utter nonsense. While the Kennedy executive order did open the door, the right of federal employees was codified by the Civil Service Reform Act of 1978 (P.L. 95-454), which you can find at 5 USC 71.
This is undoubtedly headed for court because AFGE can't afford to cede this ground without a fight. Because the TSA union does not have Title 5 recognition, the administration will prevail in the end, but we can count on leftist judges to slow things down along the way.