Frank, I'll excuse you for thinking like a man, but never tell a woman not to carry a purse if that is what she normally does, lol. While I agree that you should avoid carrying valuables in it ( passports, credit cards, cash in excess of the day's needs go into a moneybelt or neck wallet), I rarely go out without my purse in Europe. It's full of the things I deem necessary for the day- wallet, camera, phone or tablet, sunglasses, tissues, lipstick, phrase book, travel guide, etc, etc, etc.
But I'm not stupid about it either. Normal precautions - NEVER set it down. Anywhere. Even at a restaurant. Keep it closed- a snap isn't enough; it needs secure zippers. Keep it close to your body at your side or in front of you , with the flap (if it has one) against your body. I also use cross body rather than short handled purses. Never had a problem in 40 years of travel. DH, OTOH, has had 2 pickpocket incidents - one successful, both in Paris.
OP, I will agree that I don't think there are scams unique to Greece. Have your mother read Ricks warnings and recommendations on the most common ones that can be encountered anywhere.