Explanation

The time trigger used to be indicates that Eileen is no longer a picky eater, so you need a word that means something like adventurous with food. Both finicky and persnickety are nearly the opposite of what you’re looking for, so eliminate choices (B) and (F).

Choices (A) and (D) give synonymous meanings, but nothing in the sentence supports the idea that Eileen gained weight. Both epicurean and gourmandizing can mean adventurous with food, so choices (C) and (E) give you appropriate, equivalent sentences.

Hence options C and E are correct!