The submission, and the police summary of facts, said Curtis had seen Genevieve and her family water-skiing, but he did not see her fall over.
Curtis was travelling at speeds of between 25 and 30 knots (46-55km/h) shortly before he hit Genevieve.
"Genevieve ... was waiting in the water for her father to turn the boat around and retrieve her," says the police summary of facts. "She was still wearing a bright, yellow-coloured full lifejacket with head support and had her water-ski still on and sticking out of the water."
As the Lewis family turned their boat to retrieve Genevieve, they saw Curtis' boat bearing down on her, but were helpless.
"The defendant has continued to drive his boat at what is believed to be the same speed as earlier and has failed to see that Genevieve has fallen or modify his course and speed to avoid her," says the police summary of facts.
Police said Curtis told them he had seen Genevieve when he was 5-10m away and tried to take evasive action. But later trials showed the boat was easily able to avoid items in the water at 5-10m.
Witnesses told police that Curtis was not looking forward leading up to the impact, and that Genevieve was waving and signalling at the incoming boat.
Genevieve suffered horrific injuries to her upper legs and pelvis. "These injuries were described by experienced paramedics as the worst they had ever seen."
Genevieve was still alive as her father found her in the water and was screaming in pain. She was taken to shore on Curtis' boat but died on the beach.
Curtis acknowledged to the court, through his lawyer, that he had failed to keep a proper lookout. He said his visibility may have been hampered by the sun, but the harbourmaster later ruled out this theory.
Curtis was listening to music but was not under the influence of alcohol and was not using his cellphone, said police.
Genevieve's parents Guy and Rose Lewis said this week that Curtis' fine had "let our daughter, us and the community down".
"People need to be held more accountable when they take a life," the Lewises said. "Being utterly powerless to prevent her death has been one of the most difficult things to come to terms with."
They said they wanted people to understand the responsibilities they had when driving a boat or jet-ski.
By law, boats must travel at only 5 knots (9km/h) within 200m of shore or 50m from another boat or swimmer.
At their restorative justice meeting, Genevieve's parents wanted Curtis to appear with them on a TVNZ current affairs show and to make his time available to the Coastguard.
Curtis' lawyer told the court that he would not be participating in the TV show because of "his own personal torment".
"The response of the officers of the NZ Coastguard Service was to ask Mr Curtis to return to them in some months' time once the intensity of the present circumstances may have abated because, they say, his present constant reliving of the incident makes him of little use to them."
Curtis' lawyer said his client had entered the restorative justice process with the Lewises because of his "abject remorse and apology for the loss of their daughter".
Curtis is the partner of Kate McIlroy, a former world champion mountain runner and New Zealand sportswoman of the year. She was holidaying in Taupo with Curtis on the day the accident happened.
- ADDITIONAL REPORTING: Anna Leask
