Answer and Explanation:
The ethical culture that Jem and Scout show is related to the cultural and ethical values of the ancient south, where they stated that you should not treat people in ways that you do not want to be treated. Regarding money, Jem and Scout did not want anyone to take money that they lost or forgot somewhere and therefore they are in doubt whether or not to take the coins they found, because the southern ethical culture has a strong weight in their minds.
However, "finders keepers" have a very different opinion about the money that is found out there. For them, if no one manifests themselves as the owner of the money, it's okay to keep it, since you won't be stealing from anyone.