I think something along the lines of influence. Dialect kind of means accent.
It is a synonym because it is a word that means the same thing
I think the reader can most likely conclude that the speaker: Recognizes and respects her grandmother's social position
During her bath, the narrator slowly understands her Grandmother position as she grew older. If we pay attention to our society, we will see that the elderly keep losing power as they got older. They used to be listened by their children but after a certain age, the position is reserved. The children took more power over their old parents.
The best (and correct) answer choice is: [A]: "abrasive" .
_____________________________________________________
Note: In the question, the word "mew" is a typo and should be "new", methinks.
______________________________________________________