Former two-time world boxing champion Malignaggi had been helping the Dubliner prepare for the showdown with Floyd Mayweather on August 26.
But the 36-year-old American quit after he said photos posted on social media painted a false picture of the sessions.
One showed him flat on his back on the canvas as McGregor, 28, stood over him and another showed his face badly marked up.
Malignaggi, who retired from boxing in May, called on the UFC star to release footage of the spars.
Now the footage of the sparring has been posted to Twitter by UFC president Dana White - and it shows the Irishman dominating the American.
Malignaggi can be seen taking flush shots before hitting the canvas.