Officers would like to speak to the two boys as they believe they have information about the incident on Wednesday 8 March.
The two boys are white, around 11-14 years old, wearing blue jeans and trainers.
At around 10.45 on 8 March, the victim, a woman in her 60s, had withdrawn money from a cashpoint in Kingschase Shopping Centre, Kingswood, when the money was snatched out of her hands.
Following the incident, the victim received care from the ambulance service for bruising and swelling to her finger which was bent back in the incident.
If you recognise the two boys, or have any other information which could aid the investigation, call 101 and give the call handler the reference number 5223055217