Is the daughter of the husband’s mother, whether by fosterage or marriage, considered a maternal aunt (khaalah), and is it permissible to marry her?

The girl in question is not the questioner's maternal aunt; rather, she is his grandfather's stepdaughter. A stepdaughter is the daughter of a man's wife with whom he has consummated the marriage. The stepdaughter of one's father or grandfather is not considered a mahram (unmarriageable kin) to the sons or grandsons. It is permissible for a man to marry his father's or grandfather's stepdaughter, because the prohibition of marrying a stepdaughter applies only to one who has consummated the marriage with her mother, as Allah Almighty says: "And your stepdaughters, who are under your guardianship, born of your wives with whom you have consummated marriage" (Quran 4:23).

Therefore, it is permissible for the questioner to marry that girl.