BOSTON — A federal judge rejected a request Tuesday from the twin sister of mobster James “Whitey” Bulger’s girlfriend to lift a lien on her South Boston home, saying the house could eventually be used to pay a court-ordered fine for helping Bulger while he was on the run.

Prosecutors say Catherine Greig had a minority interest in the home before she transferred it to her sister, Margaret McCusker, after Greig was captured with Bulger last year in Santa Monica, Calif. McCusker lives in the home.

Prosecutors have frozen Greig’s assets in case she is ordered to pay a fine when she is sentenced next month for harboring Bulger during his 16 years as a fugitive. She faces a fine of up to $750,000.

McCusker’s lawyer, Richard Lane, argued that the lien on the home had left her unable to access a home equity line of credit.

U.S. District Judge Douglas Woodlock said he saw no reason to release the lien because McCusker does not plan to sell the house. He said the issue will be resolved after Greig is sentenced June 12.

Woodlock also questioned whether Greig and McCusker were trying to shield Greig’s interest in the property from creditors or from being seized by the government by transferring it to her sister for $1 shortly after her arrest last year. Prosecutors estimate she has a two-ninths interest in the home, which has a total value of approximately $617,500.

Lane said there was no fraud involved in the transfer.

“We weren’t concealing or hiding anything,” he said.

The judge did agree to allow McCusker to use money from Greig’s bank account to pay tax and maintenance bills on Greig’s Quincy home.

Bulger is awaiting trial for his alleged participation in 19 murders.