Elkington got roasted by the far more accomplished McIlroy.
The spat continued with Elkington insisting he "new" McIlroy was interested only in money, unlike 18-time Major champion Jack Nicklaus.
McIlroy, along with Dustin Johnson and Jason Day, made history in becoming the first top 3 in the history of the World Golf ratings to all miss a cut at the same major.
"That's why jack designed 100's of golf courses...and it's knew...mustn't have taught grammar in the 50's", McIlroy replied.
A rib injury restricted McIlroy to just six tournaments before the US Open, but he plans to play in next week's Travelers Championship and the Irish Open, Scottish Open and Open Championship in successive weeks in July.
"The worst thing I can do is go and force it because that's not my game".
For the first time since 1974, four players head into the weekend tied atop the leaderboard, with Americans Brooks Koepka and Brian Harman and English duo Paul Casey and Tommy Fleetwood locked at seven-under 137.
The 28-year-old, who has previously won the US Open, US PGA and Open Championship, needs only to win the Masters to become the sixth player to complete a career grand slam.