Is it permissible to take money from the owner of a wallet found in the mosque in exchange for returning it?

It is not permissible to take money in exchange for returning the wallet, because returning it is obligatory. However, if its owner gives something without being compelled, it is permissible to take it, due to the hadith (definition) of Zayd ibn Khalid al-Juhani regarding found items: "Recognize its container and its tie, then publicize it for a year. If its owner comes, then [give it to him]; otherwise, do as you please with it." In another narration: "If it is not recognized, then make use of it, and let it be a trust with you. If its claimant comes one day throughout time, then return it to him."