The image was uploaded to the Facebook and Instagram pages of Otley Burger Company but its owner, Joe Scholey, told Leeds Live he believes he has “done nothing wrong”.
Matthews faked the abduction of her own daughter, Shannon, back in 2008 and was jailed for eight years.
The picture of her was accompanied with the caption: “Happy Mother’s Day to all the mums out there. Don’t forget to treat them to a burger tonight.”
And, after some users voiced their concerns over its “distasteful” nature, the post was removed from the social media sites on Sunday.
One comment read: “Eh? This is in very bad taste. A bit too far this time.”
Another user said: “This is really quite distasteful and tbh (to be honest) doesn’t really do anything to promote your business to decent people.
“Please don’t bother with the ‘lighten up, it’s a joke’. “
But Joe, 28, felt those offended by this were “picking stupid fights”.
The businessman said: “We are a burger company. We literally make money from the slaughter of animals. They found this offensive, yet we profit off slaughtering living creatures.
“They seem to be picking stupid fights.
“I don’t really understand what their issue is. They have seen what we post. If they don’t like it, don’t comment. It was just a bit of a joke.”
He chose not to apologise for upsetting anyone.
“I am not apologising because they got offended,” he said.
“It does not mean they are correct. It’s perfectly legal. I have done nothing wrong.”
Otley Burger Company, based in the West Yorkshire market town, has more than 3,000 fans on Facebook alone.
It regularly shares memes, like the Matthews mash-up.
Shannon disappeared in February, 2008, while walking home from school in Dewsbury in the county.
She was found 24 days later at the home of Michael Donovan – the uncle of Karen Matthews’ then-partner Craig Meehan.
It later emerged that Karen Matthews together with Donovan were always aware of her daughter’s whereabouts. They were both jailed for their parts in the kidnapping with Matthews serving four years of an eight-year sentence before being released in 2012.
Mr Meehan was not involved in the plot.