Europe won the 2023 Ryder Cup in Rome, where Cantlay's cap stance led to home fans removing their headwear as he approached in an attempt to taunt the American.
It ultimately led to a spat between McIlroy and Cantlay's caddie Joe LaCava, who waved his cap close to the Northern Irishman as he lined up a putt after his player had holed a long effort on the 18th in a match against the four-time major champion and Matt Fitzpatrick.
That episode spilled into angry scenes in the car park at Marco Simone afterwards, which McIlroy and captain Luke Donald said fired up Europe for Sunday's singles.
"I don't think any of the 24 players on either team needs 400 grand," McIlroy said.
"Every two years, there are 104 weeks and 103 weeks you can play golf and get paid."
Europe, who have not won on American soil since 2012, will again be captained in 2025 by Donald.