Prosecutors are urging a judge to sentence James “Whitey’’ Bulger’s girlfriend, Catherine Greig, to another three years in prison Thursday for refusing to testify before a grand jury investigating whether others helped the couple during their 16 years on the run.

Greig, 65, who is already serving an eight-year sentence for helping the South Boston gangster evade capture for years, was described as “unrepentent’’ by prosecutors in a sentencing memorandum filed Tuesday in federal court in Boston.

Assistant US Attorney Mary B. Murrane wrote that Greig should serve 37 more months in prison on a criminal contempt charge as punishment “for her conscious, considered, and unapologetic violation of the law’’ and to deter others from disobeying court orders that require them to testify.

“The defendant had a choice,’’ Murrane wrote. “She could provide the testimony to the grand jury, or engage in criminal contempt and, in doing so, thwart the public interest in bringing to justice those who helped her and Bulger in their fugitive years.’’

US District Judge F. Dennis Saylor IV is scheduled to sentence Greig on Thursday.

Greig’s attorney, Kevin J. Reddington, argued in a sentencing memorandum filed last week that Greig should receive no more than six months in prison on the new charge and described her as “a kind, gentle woman who has literally done nothing bad in her life except fall in love with James Bulger and live with him for 16 years until their arrest.’’

Bulger, 86, a longtime FBI informant, fled Boston shortly before his January 1995 racketeering indictment and was joined several months later by Greig, a former dental hygienist who began dating Bulger in the 1970s and shared a house with him in Quincy.

Bulger was one of the FBI’s 10 Most Wanted when the couple were captured in June 2011 living in a rent-controlled apartment in Santa Monica, Calif. Greig used false identities, purchased Bulger’s medications, ran daily errands, and paid the couple’s bills.

In 2012, Greig pleaded guilty to conspiracy to harbor a fugitive, conspiracy to commit identity fraud, and identity fraud. She was sentenced to eight years in prison and fined $150,000.

Bulger is serving a life sentence at a federal penitentiary in Florida. He was convicted in 2013 of participating in 11 murders during the 1970s and 1980s while running a sprawling criminal organization.

In 2014, Greig was found in civil contempt for refusing to testify before the grand jury investigating whether others helped the couple while they were fugitives, and nine months were added to her sentence. She pleaded guilty to the criminal contempt charge in February.

Greig was promised immunity, which meant she could not be prosecuted as long as she testified truthfully, yet she refused to answer questions about whether anyone helped them avoid capture.

Greig could try to reduce her sentence by telling what she knows, Murrane wrote, however she “remains unrepentant for her obstruction of this information, denying the public, and Bulger’s many victims, justice for those who helped her and Bulger elude capture for 16 years.’’

Shelley Murphy can be reached at shelley.murphy@globe.com. Follow her on Twitter @shelleymurph.