Her parents have told the Parole Board they have information showing Kriel had asked their daughter out on a date and had made overtly sexual comments to her.
But Kriel denies that happened.
To resolve the matter, the board have asked the Templemans to provide the material they have.
The family will relive the trauma of a murder that stunned a nation preparing for Kriel's next appearance. His case will be called again before the end of November.
The killer was 14 when he murdered Libby.
She had been spending time revisiting friends in Kerikeri when she decided to head back into the township. Kriel accompanied her.
"It is not entirely certain what then happened. Mr Kriel provided several different versions at the time of the offending," Young said.
It seemed likely that Kriel had tripped or stumbled and pushed Libby, he said.
Kriel claims Libby was angered by this and punched him.
He then punched her several times eventually causing significant injuries.
She was rendered unconscious in the attack before he dragged her into the Wairoa Stream, leaving her face down to die.
Her clothes had also been disturbed by Kriel - which he told police was an attempt to disguise what happened as a rape.
It was called a "brutal, cruel and callous" crime by Justice Raynor Asher when Kriel was sentenced to life imprisonment for murder and indecent assault.
Kriel, now 26, has completed eight sessions with a psychologist and has a prepared safety plan.
However, the parole decision also noted he remains an "undue risk".
Young said Kriel still struggles to explain why he reacted in the way he did as to what, even if his story is accepted, was a relatively minor incident between himself and Libby.
"These are issues that will need to be further explored at the next Board meeting," he said.
Libby's mother Rebecca Templeman has declined to comment at this stage.
