"They said it was a printer error. I'm very surprised, because we couldn't use an excuse like that.
"If our dogs are out, are we going to turn around to them and say 'Oh, sorry, it was the gate's fault'?"
When she laid a complaint with the council she was told that it would take 10 days to get a response. She was also told to shred the letter, she said.
Pitt said it was not enough for the council to tell people to destroy the letters, and she believed they should collect them all.
A council spokesperson apologised and said it was taking the matter "very seriously". The council had informed the Privacy Commissioner about the error.
"Our customers' privacy is very important to us and we will be reviewing our invoicing processes so that it doesn't happen again," the spokesperson said.
The council said the error occurred while processing dog registration numbers last week.
"As a result, 354 registration reminders included details about another customer," the spokesperson said.
"We have contacted 228 customers and are still working on contacting the remaining 126 customers."