Loughlin, 55, and Giannulli, 57, "voluntarily resigned much to the disappointment of many of the members and the board," a source close to the couple tells PEOPLE.
An insider says the pair have "lost friends ever since the college scandal unfolded," adding, "People have been very critical about their actions. The backlash has been intense. They have been members of the country club for many years. Their current house even overlooks the golf course. Many of their friends are members as well."
The country club's Board of Directors had "unanimously" voted to suspend the couple's membership but that it would be "lifted after they serve their time," according to TMZ, which obtained a copy of former club president Michael Gallagher's letter in response to the decision.
"This unprecedented board decision to allow felons to continue as members causes irreparable reputational harm to the Club and its members," wrote Gallagher, who said the move would make the club a "laughingstock."
"The board action, taken on behalf of the Club's membership, now establishes our Club as a place of refuge and comfort for known felons," he wrote. "This matter is already well known in the golfing world, domestically and internationally, and our Club has become a laughingstock."
The insider tells PEOPLE that Loughlin and Giannulli were "upset" about leaving the club but "felt like they had no choice."
"The club has been an important part of their social life for a long time. They didn’t want to resign, but also felt they didn’t want to be a part of drama and hostility," the insider says. "They were upset about it, but felt like they had no choice. They didn’t feel welcomed."
On May 22, Loughlin confessed to one count of conspiracy to commit wire and mail fraud, while Giannulli pleaded guilty to one count of conspiracy to commit wire and mail fraud and one count of honest services wire and mail fraud.
Under the terms of the deal, which is still pending the judge’s approval, Loughlin agreed to serve two months in prison (though the coronavirus pandemic could affect that time), pay a $150,000 fine and do 100 hours of community service, while Giannulli agreed to serve five months, pay $250,000 and do 250 hours of community service.
Both Loughlin and Giannulli could also spend two years on supervised release.
The Full House actress and her husband became embroiled in the high-profile scandal when they were accused of paying $500,000 to Rick Singer and Key Worldwide Foundation to falsely designate their daughters Olivia Jade Giannulli, 20, and Isabella Rose Giannulli, 21, as recruits to the University of Southern California crew team, even though neither of them ever participated in the sport.
Loughlin and Giannulli’s sentencing has been scheduled for Aug. 21.
"They are spending the summer in Los Angeles with Olivia and Bella. They are still stressed about the sentencing and can’t wait for it to be over," the insider says.