The Sirsal Bankers are two bankers who run the bank on Lunar Isle. They are also two of the only three men on the island. (The third is the pirate-banker 'Bird's-Eye' Jack.) Like the women of the Moon Clan, the two bankers float behind the bank's counter.
However, after completing Dream Mentor, players can bank with 'Bird's-Eye' Jack without the seal. Talk to 'Bird's-Eye' Jack, and select "Using the bank."