The McLelland family have blamed Back and Mepham's involvement with Reiha for her death in August 2014.
The inquest heard of the "strong bond" between Back and the girl.
Lawyer Steve Manning - the local Crown prosecutor - told Hinemoa McLelland this afternoon it could be a "valid criticism" that the computer was never examined but said police were bound by the law and could not collect evidence as they liked.
Hinemoa McLelland responded that there had been "enough to get a production order for [Back's] texts" but was concerned "his home computer had never been looked at".
Manning described a meeting between investigating detective Richard Downes and the McLellands in which Downes told them of hundreds of pages of text messages obtained as part of a two-and-a-half month investigation into Back.
He said that although Downes was concerned the contact between Reiha and her former teacher at Gisborne Intermediate was a "bit dodgy" he had to explain to the McLellands he "hadn't actually found evidence of sexual offending".
The meeting, on June 20, 2014, followed concerns raised by the McLellands in early April. They were worried about reports of Back holding hands with Reiha at Gisborne Hospital, where she was being treated, and text exchanges between the pair seen by Hinemoa McLelland.
The investigation culminated in an attempt to interview Reiha at Gisborne police station with a trained female police interviewer, and an interview with Back, during which Downes pushed the former teacher over the nature of the relationship.
Manning told Hinemoa McLelland the interview with Reiha had not gone ahead - something of which she was unaware - because the teenager would not take part, beyond saying Back had done nothing wrong.
He referred Hinemoa McLelland to an email from Downes to Gisborne Intermediate in which he said the relationship with Back and Mepham had "driven a wedge" between Reiha and her parents, the same phrase used by hospital staff who had treated the teenager in early April 2014.
In other evidence today, the lawyer for Back and Mepham, Adam Simperingham, questioned Hinemoa McLelland over her basis for claiming Reiha was the victim of "sexual grooming".
He produced pages from Reiha's diary in which she wrote in May 2014: "Sam is only my best friend. He's never touched me inappropriately. He's done nothing wrong. I've completely ruined his life."
Coroner Carla na Nagara intervened after Simperingham asked Hinemoa McLelland whether her relationship with Reiha "wasn't as much of a caring and loving relationship" as the mother had thought.
Na Nagara said she had "struggled" over the way words like "blame" and "fault" had been used in the inquest, which started yesterday. "It's quite unlike any other inquest I have been involved with."
Na Nagara asked lawyers to make questions more neutral, saying the inquest was not about levelling blame, but finding the reasons Reiha died. She said she had yet to encounter a self-inflicted death which had a single cause.
Simperingham had suggested to Hinemoa McLelland that Back and Mepham provided her daughter with "emotional support" and there was no sexual aspect to the relationship.
She replied: "I hear what you're saying but why did it need to be in secret? I'm annoyed a 41-year-old man is having an inappropriate relationship with my 13-year-old daughter behind my back."
The inquest continues.
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