A is the father of B whose grandmother is C. D, the only son of C, has only one sister E who has no male child. How is E related to A's mother?

Correct option is B

A is the father of B whose grandmother is C: This implies C is the mother of A's spouse (either mother-in-law of A if B is A's biological child with another partner, or A's mother if B is from A and his spouse, and C is the mother of A).
D, the only son of C, has only one sister E: C has a son D and a daughter E.
E has no male child: E has only female children.
The search results indicate that based on the complete set of conditions, C is the mother of A's spouse, making A the son-in-law of C (or C's husband).
Therefore, E is the sister of A's spouse (D) and also A's sister-in-law.
A's mother is the mother of A. E is married to some person (not A's brother, as A is the son-in-law of C's husband) and is the mother of B (implied in some interpretations of the full problem). In the interpretation where E is A's sister-in-law, E is the daughter-in-law of A's mother.