Dina Matos’ claim – which alleged that McGreevey duped her into marriage to advance his political career – had been all that remained of the couple’s court battle after their divorce was finalized last month.

Matos issued a statement Wednesday saying she needs to bring the case to an end for the good of their 6-year-old daughter, Jacqueline.

“My former husband’s most recent efforts to keep this case in the press by releasing a letter including information about our daughter in violation of Judge (Karen) Cassidy’s order of March 18, 2008, has further underscored for me the need to bring this matter to a conclusion,” Matos said.

She was referring to an offer by McGreevey’s boyfriend to pay for Jacqueline to attend private school, which was mentioned in a letter about the case released to the media.

Matos faced a Wednesday deadline to tell the judge whether she planned to pursue the fraud claim or drop it. McGreevey’s lawyer, Stephen Haller, said both sides filed papers with the court Wednesday afternoon requesting the dismissal.

“The claim was false and merely an instrument to attempt to secure more money from Jim,” Haller said. “It failed.”

Matos alleged that McGreevey married her in 2000 even though he knew he was a closeted gay man. She later said in a tell-all memoir that she missed some obvious signs that he was gay.

McGreevey claimed his ex-wife had to have known his sexual orientation before they wed. To bolster his account, a former campaign aide came forward with a claim that he had participated in regular three-way sexual encounters with the McGreeveys for about two years before McGreevey became governor.

Matos denied that the threesomes happened.

Had the fraud claim gone forward, lawyers for both sides agree that intimate details of the couple’s sex lives would have come out. The ex-aide, Teddy Pedersen, would have been called as one of the first witnesses.

When they were divorced, the judge awarded Matos $1,075 per month in child support but no alimony. She also ruled that McGreevey owes his ex about $109,000, representing half their joint assets, and that Matos is not entitled to damages for the 13 months she would have lived in the governor’s mansion had McGreevey not resigned.

Matos offered to drop her civil claim last week, but only if McGreevey wrote her a check for the entire $109,000 and agreed not to appeal the divorce settlement. Neither of those things happened.

The couple share custody of their only child, a first-grader.

Dina Matos’ lawyer John Post said the fraud claim filed by his client will be dropped if McGreevey makes full payment and agrees not to appeal the judge’s divorce ruling.

That drew an immediate rebuke from McGreevey lawyer Steve Haller, who said, “we will appeal or not appeal at our own discretion.”

A private meeting with the judge in the case is scheduled for Monday.

Matos has claimed that McGreevey, who resigned from office in 2004 after declaring himself “a gay American,” duped her into marriage because he needed the cover of a heterosexual relationship to advance his political career.

Union County Superior Court Judge Karen Cassidy granted the McGreeveys’ divorce last month, denying her alimony but ruling that she is entitled to a portion of their joint assets totaling $109,000.

The judge did not rule on the fraud claim, which was filed separately. However, she did determine that Matos was not entitled to compensation for time in the governor’s mansion that was cut short by her husband’s resignation.

“Dina wants an end to the litigation between these parties,” Post said. “If Jim abides by the judge’s ruling, it will be over with.”

The McGreeveys’ bitter parting was evidenced during a messy four-week divorce trial in which she portrayed him as purposefully underemployed to avoid paying alimony and he portrayed her as a connoisseur of high-end clothing and other items that were well beyond her means.

The McGreeveys’ marriage publicly unraveled when he acknowledged an affair with a male staffer; the staffer denied the affair and said he was sexually harassed by the governor.

The divorce trial was held this spring after the couple failed to come to terms on alimony, child support and other financial matters. They agreed to share custody of their daughter.

A superior court judge ruled Friday that McGreevey, the nation’s first openly gay governor, must pay $250 a week, or $1,075 a month, in child support for his 6-year-old daughter with Dina Matos.

Matos had asked for $2,500 a month alimony for four years and $1,750 a month in child support. The couple share custody of the girl.

McGreevey, now a seminary student, said during the couple’s contentious divorce trial that he’s too poor to pay alimony.

In her written ruling, Union County Superior Court Judge Karen Cassidy lamented the anger and animosity she witnessed during the couple’s divorce trial.

“Especially, in a matter as high profile as this, the court was disappointed that much of the testimony, particularly as it related to public figures within the State of New Jersey, and the dirty laundry associated therewith, needed to be aired in the public and in the press,” Cassidy wrote.

“The McGreeveys clearly had agendas. As previously addressed, their anger seemed to override any ability to testify credibly or to be reasonable.”

In dividing their marital assets, Cassidy ruled that McGreevey owes Matos $109,000, representing half their various bank and investment holdings.

McGreevey abruptly resigned in 2004, acknowledging that he is “a gay American” who had an affair with a male staffer. The staffer denied the affair and said he was sexually harassed by the governor.