The two men called at the home of a 66-year-old woman in the Assynt Bank area of Penicuik at around noon on Wednesday, December 17, and arranged to carry out maintenance work on her roof.
They returned around 10am the next day and the victim paid a three figure sum in cash for a small amount of work.
The suspects then offered further work for a vastly inflated sum and asked the woman to attend at the bank to obtain more cash.
Staff at the bank then became suspicious and raised their concerns with the woman, who thereafter declined any further work on her home and refused to hand over any more money.
Officers are now urging anyone who can assist with their inquiries to come forward.
Both suspects are described as white and around six feet tall. One is in his late twenties, of thin build with short dark hair. He was wearing a dark jacket with writing on it possibly relating to a roofing company.
The other suspect is in his mid-forties of medium build with short grey hair, wearing a high visibility jacket. They were using a white van, possibly a Ford Transit.
Inspector John Dryden said: “This is a despicable crime targeting someone on their own doorstep who has been left distressed by the incident.
“We would urge anyone who has information that can assist with our inquiries to come forward. I would also remind members of our communities never to accept any offers of work on your home from unsolicited callers. If you do require any maintenance or repairs use a trusted company or individual.
“If you are cold-called and are not entirely satisfied with the authenticity of the individual at your door, do not allow them entry and do not provide any personal information or hand over any money. Should they persist then contact police immediately.”
Anyone with information relating to this incident is requested to contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111.