The team formally lodged a notification of appeal with Formula One's governing body after stewards rescinded pitlane speeding penalties handed to Alpine's Gasly at Monaco, affecting the drivers' and constructors' standings.
The U-turn, announced last week, meant Gasly returned to third place, dropping Australian Piastri from fourth to fifth.
However, four other drivers, including Piastri, had already served time penalties for the same offence earlier in the race.
George Russell lost 15 points after he fell from third at the time to 12th as he was given a drive-through penalty for failing to properly serve his pit-lane speeding penalty. His Mercedes team have sought a right of review.
Red Bull have also indicated they will appeal as Gasly's restoration meant Isack Hadjar went back to fourth from third.
Piastri is sixth in the standings, now with 68 points, 88 behind leader Kimi Antonelli. McLaren are third with 141, 121 adrift of leaders Mercedes.
McLaren said in a statement on Tuesday that while they fully respect the governing FIA's judicial processes and role of the stewards, they believe the case raises important questions about sporting fairness, regulatory consistency and the integrity of competition.
They said the removal of Gasly's penalties creates a situation in which some competitors are disadvantaged by having acted in accordance with the rules and the stewards' decisions.
The outcome risks "creating sporting inequity and undermining confidence in the consistent application of the FIA Sporting Regulations", McLaren said.
14°C