The family found the note in their letterbox without a name or return address. It was signed off by a "concerned neighbour".
The family said they were "devastated", and despite contacting their neighbours, were unable to locate the sender.
"I was devastated to know we had upset our neighbours and went to visit them to apologise personally with my children," the family said, posting to the Gold Coast Community Facebook page.
"Unfortunately they said they didn't write the letter and said they don't have any problem with noise coming from our house?"
"I wanted to let you know that we are sorry. Our son has a condition and can be a little louder than your average child," the parent wrote.
"I have been recently going through a lot personally, and was trying to get the kids outside more and away from devices/screen time."
They urged whoever wrote the note to "knock on our door" in the future, saying they consider themselves "pretty approachable people".
The parents were supported by fans of the Facebook page, who called the note's author a "gutless moron".
"Very gutless. Sign your name so the person has a chance to respond to you in person. As the (family) has clearly started, they are extremely approachable," one commenter said. "What ever happened to common decency."
"Very cowardly," another agreed.
"I would hate for this neighbour to live next to me, my eldest is very very loud," another said.
"Don't be sorry. Life happens. Don't let a passive aggressive letter ruin your day. If it mattered they would be contactable," another said.
"Congratulations on being a considerate and kind part of society. More so for being a beautiful parent. Keep doing what you feel is right for you and your children," another said encouragingly. "Kids don't come with a manual. All we can do is our best."
