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Seems to me as a retired banker, that if the “fine” is nothing more than an invitation to do business with them then they can specify how to pay which could include pigs, goats, chickens or anything they want and you either accept that or decline to contract with them.
On the other hand, if it is to discharge a debt, then they must take any lawful form of currency, including a BOE and, if you sent them one and they kept it then they have accepted payment for the debt and the debit is discharged, but if they send the BOE back to you then they have refused payment for the debt so the debt is now wiped clean!