Jay Leno -- NBC Quickly Wipes Away His Memory

NBC is already distancing themselves from Jay Leno ... by erasing his name off the side of the building where he shot "The Tonight Show."

The Peacock network sent a team of painters armed with rollers and a forklift to white-out Jay's billboard -- just ONE FRICKIN' DAY after he signed off for good.

Here's what's interesting ... Jimmy Fallon's moving the show to NYC, so the net's not really under a deadline to change the signage before Jimmy takes over the reigns. Guess they just wanted to let Jay know that this "goodbye" is permanent.