The correct answer is (E).
Charlotte certainly seems to go out of her way to be nice, so the best way to approach this sentence to find a word that means "overly nice" or something similar.
Because (A) "artless" means "ignorant" or "innocent" and has nothing to do with being "nice," we can eliminate this as a choice. (B) "random" (without careful course of action) and (C) "fraudulent" (deceitful or dishonest) do not fit her description either. Her compliments may or may not be out of place, which is what choice (D) "anachronistic" means, but we are looking for a word that describes Charlotte's personality as being "overly nice." The correct choice is (E) because "obsequious" means "overly submissive and eager to please," exactly the type of person Charlotte seems to be.
