The embarrassing blunder came after locals noticed the company had completely covered iconic local work "It's like a jungle sometimes," by Colin Bebe with an advertisement for film.
Pictures of the reworked mural containing the #mothermovie hashtag were shown online after being defaced by someone apparently unhappy about the piece of advertising in the street.
The company said it had talked to the original artist, who asked the team finish their mural and make the latest incarnation "another chapter in the story of this mural".
"In the meantime, he has asked that we finish our mural. He is supportive of what we do and understands that we are a collective of sign writers who employ artists to do what they love doing - we are not a faceless corporate entity," the company said.
"After we complete the final stage of this mural, we are going to restore the original mural in collaboration with the artist and we have agreed to cover all costs, assist him in painting it and get the story of the mural out there to as many people as we can. We are also going to use this opportunity to raise money for a local charity of the artist's choice to raise awareness around youth suicide."
The post attracted international media attention and comments from locals who showed mixed reaction on the issue. Some couldn't understand why the company, which specialises in handpainted signs, would cover another artists work, while others said the outrage was misguided.
A Newtown local known as Jetta wrote on Instagram: "I was heartbroken when I saw this on the weekend. Thank you for recognising the gravity & seriousness of what you have done. It's a relief to hear it's being rectified."
Another user known as Phil said "this post is definitely the best way to go about righting that mistake. Good on you guys, and props to the original artist for being understanding about it. Can't wait to see the new mural once it's done!"
The Inner West Council posted on Instagram that it did not approve the advertisement which would be prohibited in a heritage area.
"The matter is now being investigated by Council's Compliance Section," it said.
