The couple had accused New Jersey's flagship public university of failing to prevent their son's suicide in 2010, which occurred just days after the webcam spying, and had filed court papers preserving their right to sue.
But Mainardi said the Clementis felt that Rutgers had been "very responsive" and that the school was working with the Tyler Clementi Foundation on a number of projects.
"They've met with us a number of times at the highest level," the attorney said. "They have undertaken a lot within the university system to respond to this voluntarily, responsibly."
Rutgers changed its housing policies after Clementi's suicide, allowing opposite-sex roommates, with the idea of making gay and lesbian students more comfortable.
The Clementis' foundation has been a cosponsor of an academic conference at Rutgers on social media.
The family has said it wanted the foundation to teach responsible use of social media and to increase acceptance of gays in schools, communities, and even churches.
Tyler Clementi jumped to his death from the George Washington Bridge. His roommate, Dharun Ravi, spent 20 days in jail last year after being convicted of bias intimidation, invasion of privacy, and witness tampering. He is appealing.
Ravi was not charged with causing Clementi's death, but his family has said they believed his behavior was a factor, especially in light of tweets he made that were part of the case against him.
One of them read, in part: "I saw him making out with a dude. Yay."
Clementi had told his parents he was gay before leaving college, three weeks before his death. But they believe that learning about the webcam recording in his dorm room humiliated him and made him realize that being out as gay on campus would not be so easy.