The former socialite's lawyer, Bobbi Sternheim, argues that Maxwell is facing tougher jail conditions than inmates convicted of murder or terrorism.
In her submission, Sternheim said the frequent checks were unnecessary, as Ghislaine Maxwell had no history of suicidal thoughts.
In her request, Ms Sternheim made no direct reference to Epstein taking his life in August 2019 in his cell at another federal lockup, in Manhattan.
Sternheim requested that US District Judge Alison Nathan order the MDC's warden to address the court regarding the conditions of Maxwell's detention. Prosecutors declined to comment.
A lawyer for Maxwell, 58, didn't immediately return an email seeking comment.
The government said she will not be able to meet with her lawyers during quarantine as she prepares for a July trial on charges alleging she recruited three teenage girls for Epstein to abuse in the 1990s.
Maxwell has been held apart from the prison's general population in an isolation cell but she has for about three months been allowed out of the cell from 7 a.m.to 8 p.m. every day.
The letter is in response to a filing from federal prosecutors on Monday, informing the judge that Maxwell had a Covid-19 scare following possible exposure to an infected staff member at the Metropolitan Detention Center, and had been placed in quarantine.
Maxwell, prosecutors continued, has had ample time to review the evidence, compared to other inmates with cases pending.
The letter from federal prosecutors claimed that Maxwell had received better treatment than other inmates during her brush with a COVID-19 infection. Specifically, on November 18, 2020, the defendant was tested for COVID-19 using a rapid test, which was negative.
Jeffrey Epstein and Ghislaine Maxwell attend de Grisogono Sponsors The 2005 Wall Street Concert Series Benefitting Wall Street Rising at Cipriani Wall Street on March 15, 2005 in New York City.
The lawyer said Maxwell is kept in what is, in effect, solitary confinement and she is excessively and invasively searched and monitored 24 hours a day, including camera surveillance in her cell and a camera following her movement whenever she is permitted to leave her cell.