Following Delta policy exactly does not guarantee you will not be arrested in NYC and charged with a felony which they usually downgrade to a misdemeanor with a high fine ($thousands) and gun confiscation. A lot of tourist get trapped this way in NYC because the will call police to check that the gun is legal in New York.

The reason for all this is that the gun must be licensed in New York. A Tourist checks a gun legally elsewhere and flies to New York, gun is delivered, they conduct there business and goes back to check in. The GA will call the police to check if the gun is legal in New York. If not you go directly to jail. So be prepared to show the gun is registered in New York and carried to the airport legally per New York law. Then be prepared to prove all this to the cop.