FWIW, J. Gavin Scott, in British Countermarks on Copper & Bronze Coins (Spink, London, 1975) lists an MB counterstamp on a halfpenny 1799 (catalog number 123.211) and notes that "this countermark is included, as Christopher Brunel reports that he has seen two examples, presumably from the same punch". He thinks it is a token or a shop ticket.
As the listed piece is not illustrated, I can't guarantee that your MB was made with the same punch. The second set of initials was almost certainly added later, by someone who didn't have letter punches.
Peter