She said a woman claiming to be an Israeli named Heidi and a Russian man called Michael knocked on her door on January 6.
Ms Arthur says the pair were asking for $140 to $180 per painting.
Police say the paintings can be bought online for just a few dollars each but Ms Arthur said the pair gave a very credible sales pitch.
"She said that she had met up with an Israeli gentleman in Christchurch who offered her a door-to-door job selling these artworks as a way of making some money while she is on holiday in New Zealand with her boyfriend."
Ms Arthur said she had no money to pay for a painting depicting a horse-racing scene.
The pair said they needed cash upfront, and even offered to babysit her daughter while she went to an ATM.
"I then said I had no money until Tuesday anyway, ATM or not," Ms Arthur said.
"At which point they left the painting and said they were going to Christchurch, and I would send the money to my sister there and she would pay them for me."
Ms Arthur took a photo of two paintings. She said 'Heidi' was careful to crouch down behind the picture while it was taken.
Once the pair left, she wondered whether she was the target of a scam.
A quick internet search confirmed her fears and she did not return the tricksters' calls.
Ms Arthur described the woman as being in her early 20s, with long blond hair in a ponytail. She was wearing a white top and tight black pants and spoke with a French accent.
"She told me she was an Israeli though her mother was French."
'Michael' was medium height and build, with black hair. He was wearing a white t-shirt, baggy jeans and a silver nose ring.
Police today confirmed a couple were caught in the Cashmere area of Christchurch yesterday after receiving a report earlier this week of people going door to door trying to sell the paintings.
"These groups have been active in Christchurch recently," said acting inspector Glenn Nalder.
"This scam has been ongoing for over ten years now, in New Zealand and around the world.
"I'm aware of it happening in other parts of the country. They're very mobile by their very nature and can pop up anywhere at anytime.
"Inquiries are continuing in relation to the man and woman spoken to - and we have not ruled out charging the pair."
Descriptions of the Dunedin couple match the Christchurch pair, he said.
Obtaining by deception is punishable by up to seven years in prison and police say they will also be sharing information with the New Zealand Immigration Service.
"Often the scammers are in breach of immigration regulations," Mr Nalder said.
Police urge residents to turn away people selling art door to door.
"My advice to people is that they are free to purchase the paintings if they wish, but they need to be aware that they can go online to any one of a dozen websites and buy them direct from the wholesaler in China for a few dollars," said Mr Nalder.
