Trying To Sell It
Considering the precarious financial situation Eleanor was in, she opted against just tossing the rock in the garbage and instead chose to take it to a jewelry shop. Even though she was aware of its low value, she hoped the jeweler would still be willing to buy it from her.
Nothing To Lose
What did Eleanor have to lose, even though it felt like a strategy bound to failure? She could still easily toss it away if nobody was interested, and she wouldn’t have spent more than a day. Which she otherwise would have likely spent replying to employment applications that would not have gotten back to her.