She is the third person to be stung by telephone fraudsters in the past month.
The woman, in her seventies, received bogus calls yesterday from a man claiming to be from Scottish Borders Council.
He told he she was due a council tax refund and asked for her bank card details.
These were shared and the woman later discovered a low three-figure-sum of money had been taken from her account.
A Scottish Borders Council spokesperson said: “Council officers or their agents may contact residents by telephone to discuss unpaid council tax and may accept payment over the telephone.
“However, this will have been preceded by written confirmation of the unpaid council tax.
“They will also have full details of the account and will never insist on payment being made by telephone.
“Residents should be extremely wary of unsolicited phone calls and if in any doubt should not give out personal details and contact the council via the customer services Tteam on 0300 100 1800.”
Police Scotland is urging Borderers to remain vigilant.
Police constable Nick Walker said: “Please be very wary of unsolicited phone calls and never give personal details including bank or credit card details.
“Terminate the call and contact the organisation using the number you would normally contact them on not the number given by the caller.”