What is the ruling on greeting my mother’s maternal aunt?.
Your mother’s maternal aunt is also a maternal aunt for you. And you are a mahram for her, so there is nothing wrong with your shaking hands with her.
Allaah says, explaining who is a mahram (interpretation of the meaning):
“Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters…”
The word khaalah (mother’s sister or maternal aunt) in the verse includes the maternal aunt of one's father and mother, and grandfathers and grandmothers, and the same applies to paternal aunts.
Al-Sa’di said (p. 244):
‘Ammah (paternal aunt) refers to the sister of your father and grandfather, no matter how far the line of ascent reaches, and khaalah (maternal aunt) refers to the sister of your mother and grandmother, no matter how far back the line of ascent reaches. End quote. See also Tafseer al-Qaasimi, 5/86
It says in Zaad al-Mustaqni’, when discussing which woman are mahrams: Every paternal aunt and maternal aunt, no matter how far back they go.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in his commentary: “No matter how far back they go” means the maternal and paternal aunts of one's father, or the maternal or paternal aunts of one’s mother, or the maternal aunt of one's grandmother, or the paternal aunt of one’s grandfather or grandmother, and so on ad infinitum. End quote from al-Sharh al-Mumti’, 5/184.