Jordan McSweeney, 30, sexually assaulted and killed Zara, 35, as she walked home from a night out with pals.
He got life in jail with a minimum of 38 years but yesterday appealed for a reduction.
His barrister argued the murder in Ilford, East London, in June 2022, was not premeditated.
Zara’s aunt Farah Naz told the Court of Appeal that his application had caused “profound distress” to her family.
She said: “It is beyond belief that this individual, who was too spineless to attend his own sentencing, has the audacity to appeal the very sentence he couldn’t be bothered to witness.”
McSweeney appeared for the start of proceedings via videolink from Long Lartin prison in Worcestershire, but left before the hearing was completed.
Around 45 minutes after the hearing started it was paused and a prison officer, who appeared on the link with McSweeney, said: “He’s heard enough and has got everything he requires in his cell.”
Ms Naz said this behaviour had underscored the killer’s “enduring disregard for all”.
Appeal judges said they will give their decision “as soon as possible”.