<em>Unrequited</em> refers to something that is not returned or reciprocated. It is often used in the context of love, to describe a situation in which a person loves someone who does not love him back.
<em>Toil</em> refers to extremely difficult and exhausting labour, often physical.
"Unrequited toil" most likely refers to very hard, tiring work for which the person does not gain anything in return.
because it would be the quickest way for Jeb to find out if the article called A Look Back at the Civil War contained any information on robert e. lee.