A tackle on the same player three minutes later saw Cleveland Taylor pick up his second booking of the game to join Byrne in the dressing room.
But Iron boss Nigel Adkins reckons Byrne should not have been sent off.
"I have seen the video and Cleveland Taylor is fouled by their player (in the build-up). It is a foul. Period," he insisted to the Scunthorpe Telegraph.
"Byrne then makes a challenge on the player. The player is not touched. His momentum makes him fall over and Byrne is sent off."
United hope Byrne will be available to play at Cheltenham Town on Friday night.
If the appeal is unsuccesful then he will have to sit through a three-match suspension.