The lawyer representing Rachel Canning's parents made the request during a news conference at his Roseland office on Wednesday.
Angelo Sarno said the 18-year-old's return is not contingent on any financial or other considerations. He said the suit had been settled "amicably," but refused to comment further on the litigation.
Sarno said the notoriety surrounding the suit had done damage to the family, and they are asking for privacy.
A judge last week had denied the teen's request for child support and to have her parents pay her remaining high school tuition. But the judge scheduled an April court date to consider the over-arching question of whether the Cannings are obligated to financially support their adult daughter.
State Superior Court Judge Peter Bogaard sounded skeptical of some of the claims in the lawsuit, saying it could lead to teens "thumbing their noses" at their parents, leaving home and then asking for financial support.
"Are we going to open the gates for 12-year-olds to sue for an Xbox? For 13-year-olds to sue for an iPhone?" he asked. "We should be mindful of a potentially slippery slope."
Canning had left her parents' house on Oct. 30, two days before she turned 18 after a tumultuous stretch during which her parents separated and reconciled and the teen began getting into uncharacteristic trouble at school.
In court filings, Canning's parents, retired Lincoln Park police Chief Sean Canning and his wife, Elizabeth, said their daughter voluntarily left home because she didn't want to abide by reasonable household rules, such as being respectful, keeping a curfew, doing a few chores and ending a relationship with a boyfriend her parents say is a bad influence. They say that shortly before she turned 18, she told her parents that she would be an adult and could do whatever she wanted.
She said in her lawsuit that her parents are abusive, contributed to an eating disorder she developed and pushed her to get a basketball scholarship. They say they were supportive, helped her through the eating disorder and paid for her to go to a private school where she would not get as much playing time in basketball as she would have at a public school.
Rachel Canning had been living in Rockaway Township with the family of her best friend. The friend's father, former Morris County Freeholder John Inglesino, was paying for the lawsuit.