"It was done to intimidate," Connolly told NPR. "No question about it."
It wasn't the first time a disturbing incident took place as the publication investigated Epstein.
Connolly also told NPR that Epstein himself showed up at the magazine's office in 2003 after reporter Vicky Ward began probing Epstein's wealth and links to young women.
During her investigation, Ward interviewed Annie and Maria Farmer, two sisters who claimed they had been abused by Epstein.
On the day Epstein was spotted at Vanity Fair's headquarters, he was there to pressure the editor into abandoning the story.
That's according to Connolly, who said Epstein was "torturing Graydon" in person and via a number of phone calls.
A subsequent Vanity Fair article on Epstein made no reference to the Farmer sisters — but soon after it was published, Carter found a bullet on his doorstep, which Connolly said "wasn't a coincidence".
"Even in the absence of any evidence Epstein was involved, Connolly says, both Carter and he considered the bullet a clear warning from Epstein," NPR's David Folkenflik writes.
"Another former colleague, who spoke on condition of anonymity, recalls receiving an anguished call from Carter linking the bullet to Epstein."
The Farmer sisters told NPR Vanity Fair's decision not to publish their claims was "terribly painful", although the magazine insisted their allegations were excluded for legal reasons only and not as a result of intimidation.
In a statement sent to the New York Post, Carter claimed Vanity Fair had never decided to abandon a story over threats.
"During my 25 years at Vanity Fair, we took the legal requirements for reporting incredibly seriously on every story, particularly pieces in which the subject was a private person and therefore rigorously protected by libel laws," the statement reads.
"And the fact remains that Ms Ward's reporting on this most important topic did not meet our legal threshold when we published the piece in 2003.
"In subsequent years, I received numerous personal threats — including, on separate occasions, the delivery of a bullet on my doorstep and a severed cat's head in the garden of our weekend house. There was no investigation and I have no idea who was responsible …"
Carter said there was no proof Epstein was involved in planting either the bullet or the cat's head, and said he wasn't even sure when he found the bullet at his home.