Trainer Willie Mullins was fined €200 and the horse prevented from running for two days after Devils Bride was a late absentee from the Premier Jump Weekend Hurdle due to a change in the going.
The local stewards felt the ground had not altered enough to justify the decision.
It meant Devils Bride could not run in the following day’s INH Stallion Owners EBF Novice Hurdle at Thurles, for which he was declared and would have been a leading fancy.
O’Leary said the matter was now closed.
“It’s all resolved. We had a meeting with them (Irish Turf Club) on Friday. It went very well, we’ve withdrawn the appeal,” the leading owner and chief executive of airline Ryanair said.
“We’ve clarified our understanding of the rules and if there’s a change of ground, the horse won’t be fined in future.
“We understand the rule a little bit better, so there’s no need to go ahead with the appeal.
“I don’t want to be fighting with the Turf Club. It’s a hobby, so let peace reign.
“You’re declaring horses on Friday depending on what the ground is like on Sunday and the ground in Ireland can change materially over a two-day period.”
The appeal withdrawal came a few days after Gigginstown were cleared of any wrongdoing by the Turf Club in an unrelated matter concerning the late scratching of Road To Riches at Cork on November 3.