Praise be to Allaah.
You are not allowed to shake her hand or to kiss her on the head or anywhere else. What is allowed is for you to greet her with words only, even if she is old, because she is not your mahram. There is nothing wrong with you saying, “How are you? How are your children?” etc. The Messenger (peace and blessings of Allaah be upon him) said: “I do not shake hands with women” – and this included old women as well as others. And ‘Aa’ishah (may Allaah be pleased with her) said: “By Allaah, the hand of the Messenger of Allaah never touched the hand of any woman” – meaning women who were not his mahrams, and when he accepted their oaths of allegiance to him, it was by words only.