Hope died in January after being sent to Starship Children's Hospital in critical condition. A decision was made to turn off her life support days later.
It was earlier reported that Hope spent the first months of her life in the neonatal unit at Dunedin Hospital after she was born at 27 weeks, on August 25 last year.
"She [Hope] was a wee angel," her grandmother, Sharon Schultz, told the Otago Daily Times.
Detective Sergeant Mark McCloy last month thanked the Invercargill community and Hope's family for their assistance and patience during the police investigation.
At Wallis' initial appearance, Vesty sought bail on several grounds, which police did not oppose.
Judge Tony Zohrab said then that having heard the lawyer and having read the affidavit from the man's family that bail was appropriate on a set of strict conditions.
Wallis was remanded on bail to live with relatives in Nelson on those strict conditions.
Justice Mander today further remanded Wallis on bail on the existing terms, to a call-over on June 14.
A date was set for the trial to begin on July 31, 2023.