But the Arabs have ruled out their own challenge, saying they think they have no hope of overturning their defender's dismissal.
Scotland midfielder Thomson and former Motherwell centre-half Gunning were both shown straight red cards midway through the second half of Saturday's 1-1 Scottish Premiership draw at Easter Road.
The Hibs midfielder reacted angrily after he was caught by Gunning's follow through as they challenged for a bouncing ball on the edge of the United box.
Both men went head-to-head as a scrum of their respective team-mates raced in to pull them apart.
They even had to be separated once more as they made their way off the pitch.
Hibs are confident their man did not land any punches and have paid the £1,000 fee to lodge an appeal with the Scottish Football Association.
A spokesman for the Leith side said: "Hibernian can confirm that following the review of the TV footage of the match versus Dundee United at the weekend the club have notified the Compliance Officer at the Scottish FA of our desire to lodge a Player Reference for Wrongful Dismissal against the red card shown to Kevin Thomson.
"Footage together with the grounds for the referral will now be submitted to the Compliance Officer prior to the 3pm deadline on Tuesday."
United believe neither player should have been shown any more than a yellow card following the incident but have decided against appealing referee Crawford Allan's decision.
The club's official Twitter account posted the following statement: "No Gavin Gunning appeal to be made. Club feel that whilst the red card appeared harsh, the chance of it being overturned is low."
United were a goal up through Stuart Armstrong's opener when the fracas erupted with 65 minutes gone.
But the sending-off appeared to help Hibs find their fighting spirit and they battled back to earn their first point of the season thanks to Scott Robertson's equaliser nine minutes from time.