Thrash, however, rescinded Ogunjobi's fine of $10,527.
Ogunjobi had been disciplined for shoving Mason Rudolph from behind during last Thursday night's game after Browns teammate Myles Garrett had hit the Pittsburgh Steelers quarterback on top of his head with Rudolph's own helmet.
The NFL said rulings on the appeals by Garrett and the Steelers' Maurkice Pouncey will be issued later in the week.
Garrett was given an indefinite suspension of at least six games for striking Rudolph, while Pouncey received a three-game ban for kicking and punching Garrett.
Rudolph called Garrett's actions "bush league" and "cowardly" during his news conference following Pittsburgh's 21-7 loss to Cleveland.
Appeals officers are jointly appointed by the NFL and the NFLPA. Thrash also conducted the hearing for Garrett on Wednesday, and Derrick Brooks heard the Pouncey appeal Tuesday.