I believe that Eurycleia doesn't want Telemachus to leave because she doesn't want to leave the palace unprotected.
She believes that if he leaves, the suitors will try to plunder the palace and steal everything, and there will be no one to protect either the palace, or Penelope.
The answer is their because "the girls" is plural, meaning more than 1 girl is being addressed. Therefore, the answer cannot be her.
The answer would be A. An attention grabbing sentence.
For sure W because nobody at the time knew why people did these type of things