Answer by Rabbi Chaim Hillel Raskin – a rov in Kfar Chabad Beis:
The responsibility to return a lost object to another Jew is both a positive commandment of hashovas aveida and a prohibition not to hold on to it.
In fulfilling this obligation, one is required to invest all his efforts, but is not required to spend money.
Halacha states that one who encounters a lost object must return it without charge, since one is merely fulfilling a mitzvah. However, since one isn’t required to lose money, he may demand compensation of whatever money he put out to retrieve the object (e.g. tow a car).
Likewise, one who takes time off work to return an object, may demand “schar batala” payment for that time.6 Schar batala is calculated as the amount of money he would accept to take off work and not earn his regular income.
Can the owner offer a monetary reward?
Many poskim write that although the finder may not charge, there is no prohibition for the owner to set a reward. Some explain that special allowance was made here to encourage people to actively search for the lost object. Others draw a comparison to a mohel who halacha permits to charge so that he will perform a skilled job.
Still, other poskim argue there is a broad prohibition to accept payment for returning a lost object. Thus in practice, a finder should reject the payment, and if the owner insists that he accept it as a gift, he may accept it.
In situations where returning the lost object is an act of lifnim mishuras hadin (beyond the exact law), such as an object that was found in a place where the majority of the passerby are not Jewish, one may accept payment.