Matt Reeves reveals some details behind Barry Keoghan's Joker, the deleted scene he alludes to here has just been released, while talking about the character Reeves said, "It's like aPhantom of the Opera...He has a congenital disease where he can’t stop smiling and it’s horrific. His face is half-covered through most of the film...It’s not about some version where he falls into a vat of chemicals and his face is distorted, or what [Christopher] Nolan did, where there’s some mystery to how he got these scars carved into his face,” Reeves further said. “What if this guy from birth had this disease and he was cursed? He had this smile that people stared at that was grotesque and terrifying. Even as a child, people looked at him with horror, and his response was to say, ‘Okay, so a joke was played on me,’ and this was his nihilistic take on the world.”
Reeves has said that Barry's Joker has been a bit inspired from David Lynch's The Elephant Man and Barry Keoghan's character is yet to fully become the Joker just like other characters in this Batman Universe. They're still developing and evolving in their roles.

It's going to be interesting to see more interactions between the Clown Prince of Crime and the Caped Crusader in the future.