"He loved company. He always wanted to come in," Mrs Green added. The couple tried to set it free, driving to Pahoia where they released it, but it returned to their home.
"He beat us home," Mr Green said.
In the evenings the pigeon would roost on the neighbour's roof, returning each morning for breakfast.
The Greens said they had a good relationship with their neighbour and hosed the roof down each morning where the bird had left its mark.
But one morning when Mr Green called his "mate", it didn't come.
When he looked over at his neighbour's house he found "Pidgey" slumped in the gutter, a trail of blood on the roof marking its descent.
"He was still warm and bleeding," he said, sadly. "He had been shot by some vicious person with a pellet gun. It broke my heart."
The neighbours heard a shot at about 4.15am, he said.
"It must have been someone who lives near me to see him on the roof. The person might brag about what they have done. I hope they are overheard," he added.
"They're vicious people who do things like that. They have no love for life. I miss him so much."
Tauranga police Acting Senior Sergeant Cameron Anderson said police had questioned residents in the street but had not identified the person responsible.
He cautioned against using slug or soft air guns in residential areas.
"If you don't know what's behind the intended target ... it could possibly hit someone," he said. "We attend numerous jobs a year where people are firing slug guns and air rifles in the backyard."
The Arms Act states that anyone who discharges a firearm, air gun, pistol or restricted weapon in or near a house "without reasonable cause ... so as to endanger property or to endanger, annoy or frighten any person" could face up to three months in prison and/or a fine of up to $3000.