The hospital worker transferred the presenters, believing they were the Queen and the Prince of Wales, to a colleague who described in detail the condition of Kate during her treatment for severe pregnancy sickness last Tuesday.
Tragic Ms Saldanha, an Indian native who lived in Bristol, England, was found dead three days later in a block of nurses' flats close to the hospital.
British MP Keith Vaz met the nurse's family last night and said they had been left "devastated".
The family also visited the King Edward VII's Hospital and a memorial service will be held this week.
Flanked by Ms Saldanha's husband Benedict Barboza, her daughter Lisha (14) and son Junal (16), Mr Vaz said: "They just want me to say that they are extremely grateful to the public in the UK and throughout the world who have sent them messages of condolences and support following the death of Jacintha -- a loving mother and a loving wife."
The nurse's brother Naveen said his sister was a devout Catholic and would have been "devastated" by her unwitting role in the breach of medical confidentiality.
Barboza expressed his sadness on his Facebook page with a short note "Obituary Jacintha."
"I am devastated with the tragic loss of my beloved wife Jacintha in tragic circumstances," he wrote.
He said she will be laid to rest in Shirva, India.
Mr Vaz has called for the hospital to provide the family with more support and to hold an inquiry.
Scotland Yard said it was likely an inquest would be opened and adjourned at Westminster Coroner's Court later this week.
The death is not being treated as suspicious.