Terrell Davis' camp just released new footage of his recent run-in with law enforcement aboard a United Airlines flight ... which they believe proves several agents acted in the wrong.

The Hall of Famer's attorneys shared the video with TMZ Sports on Tuesday ... showing the Denver Broncos legend pulled off the airplane by responding officers -- including the FBI.

In the clip, passengers are heard questioning what led to the removal ... with TD's wife, Tamiko Nash, standing up and interacting with the agents before he was placed in handcuffs and escorted off the plane for questioning.

Davis' team says the brief clip backs their claim that Davis was wrongfully detained ... and made it clear they're taking the matter to court.

"This video confirms the harrowing tale of multiple law enforcement agents, including the FBI, boarding the plane and apprehending a shocked, terrified, humiliated, and compliant Mr. Davis in front of his wife, Tamiko, minor children, and more than one hundred passengers," Davis' attorney, Parker Stinar, said in a statement.

"The rationale behind the United Airlines employee's deceitful or inaccurate report extends far beyond a mere ice request or innocent tap on the shoulder."

Davis' team added the lawsuit will bring the truth to light ... and force United to address the "systemic shortcomings that culminated in this traumatic incident, causing irreparable harm and enduring suffering for the Davis family."

As we previously reported, Davis and his loved ones were aboard a flight from Denver to Orange County on July 13 ... and during the trip, he says he tapped a flight attendant on the shoulder to request a cup of ice.

The former running back then said the attendant snapped on him ... saying, "don't hit me," before darting to another part of the plane.

After touching down in California, Davis was rushed off the plane and questioned ... but said the agents later apologized and threw their support behind him.