The Mudd replicants that lose are arm very clearly have the actor just tucking his arm inside his clothing.
Mudd states that any fortune he may have once had was taxed away by the Federation. The Federation does not collect taxes as it does not use money at all. While this could be attributed to a ruse on Mudd's part, the Tellarite bounty hunter does not question this part of his story. Tellarites are also part of the Federation. Even if individuals like Mudd and the bounty hunter choose to live outside the Federations economic system for whatever reason, they would still be aware of how it functions.