"I would implore you to consider taking action which would finally bring this matter to a close as an act of mercy for myself and my family," the 54-year-old told Los Angeles Superior Court Judge Scott Gordon, reading from a statement.
"I do not want to have to explain to my granddaughter why she can't go outside or answer the phone or why there are cameras outside the home and eventually what happened to her nana in 1977."
In her first appearance in court in the case against the 83-year-old Oscar winner, Geimer told the judge he could explore various avenues to settle the matter, including dismissing it, sentencing Polanski to time served or recalling an international arrest warrant against the director.
Gordon could also unseal documents that Polanski claims prove he had struck a deal with the initial judge in the case.
"Your words mean a lot to this court," the Los Angeles judge told Geimer.
Victim condemns Polanski's treatment
Geimer was accompanied by her husband of nearly 30 years told reporters that Polanski is now facing the same type of abuse that she endured after the assault.
"When this happened, my mother and I were [treated] as lying gold diggers who were attacking poor unfortunate Roman. It was a much different story," she said. "Now everyone calls him a paedophile and says terrible things about him that aren't true."
Polanski's attorney Harland Braun also filed a motion to dismiss the case on Friday saying his client had served time for his crime.
The filmmaker admitted statutory rape after the more serious charges that he drugged, raped and sodomised the teen were dropped, and spent 42 days in custody to undergo psychiatric evaluation before being released.
He fled to France in 1978 because he believed a judge was going to back out on a deal to treat that as time served.
The prosecutor objected to the motion.