My father married a woman (who is not my mother)―Am I allowed to shake the hand of my father’s mother-in-law? Imām Ibn Bāz

A questioner asks about the allowance of shaking the hand of his father’s mother-in-law from his second wife.

Answer: Your father’s mother-in-law (from his second wife) is not your mahram^[1]. Rather she is mahram to your father because she is the mother of his wife. So she is not the mahram of his son^[2]. Only the father’s wife is a mahram to his son, meaning, your stepmother is a mahram for you. As for your father’s mother-in-law (from his second wife), then she is a mahram for him. Likewise, your grandfather’s mother-in-law (from his second wife), then she is a mahram for your grandfather―but she is not a mahram for you because she is a non-relative to you.

Source: Fatāwa Nūr ‘alad-Darb of Shaikh Ibn Bāz, vol. 31, p. 311 (no. 134), Q. 5, Audio no. 239.

[1] Meaning, she is not like your actual grandmother.
[2] Meaning, son from his from his first wife.