The victim was visibly upset about the incident, he said.
"She already felt sad visiting her parents' grave, but then this happens. This is about as low as you can go."
Const Gilbert said the woman did not get a look at the thief, but was helped at the scene by two men.
Police believed the person lived locally and inquiries were continuing.
However, he urged the person to deliver the handbag to police, "or let us know where we can pick it up - no questions asked".
"If he wants the cash, that's fine, we just want her property returned."
The incident also served as a reminder for people to secure their vehicles and stay vigilant, even in cemeteries.