Sara Trumble wants compensation after allegedly being unfairly dismissed from her job as a nanny after she became pregnant.
Mills' split from the former Beatle in 2006 was followed by a messy divorce in which she won 24 million pounds - some of it intended to pay for a nanny for their daughter, Beatrice.
Mills was criticized in the divorce judgment, which called her "less than candid."
The lawyer for 25-year-old Trumble, Nick Fairweather, argues that the judgment should be introduced as evidence of Mills' dishonesty.
Mills' lawyer argues that would prejudice the trial. The hearing was adjourned Monday while a judge considered Fairweather's request.
