The warning comes after an Annan woman was the victim of a theft at Aldi on Tuesday.
At around 1.40 pm, the 74-year-old woman completed her shopping by paying for it by debit card, having to key in her four digit code.
On leaving the store she was approached by a male and a female, who spoke little English, indicating that she had dropped a £5 note from her purse in the store.
As the victim opened her purse to check, the woman began pointing into the purse. The two parties then separated.
And the following day, the pensioner discovered that her debit card had been stolen, believing all likelihood during this meeting with the two at Aldi.
On checking with her bank it was discovered that the card had been used a number of times immediately after she met the two at Aldi.
Constable Victoria Urwin at Annan said: “It does appear that the shopper has been the victim of a distraction theft by the man and woman who approached her after leaving the Aldi store.
“The use of the card also indicates that these two, or others working with them were monitoring the lady as she keyed in her pin number at the till.
“We are currently examining CCTV to look for evidence and a better description of the two who approached the lady.”
The couple are so far only described as speaking what may have been Italian.
PC Urwin added: “Again we would urge those using cash machines or keying in their pin number at tills to be vigilant when doing so.
“We are asking anyone who may be able to help us in this enquiry to get in touch with us at Annan on the 101 number, quoting reference number PDG 0146830718.”
And now, a second theft has been reported.
On the same day, around 20 minutes later, a 67-year-old woman from Langholm left the store, having paid for her shopping with a debit card, using her PIN number.
On leaving the store, she was approached by a man who indicated that she had dropped a £10 note in the store.
On opening her purse to check she confirmed that she had not lost the note.
However, it now transpires that at some point her debit card was stolen, and used a short while later in the town to withdraw money from the cash machine at the Bank of Scotland in the High Street.
Other transactions using the card have been rejected by her bank.
Anyone who can help catch the thieves should call police on 101 and quote the reference number PDG 0146830718.