Okay so Tierra has banknotes, which is what will make this process easier. Because of the banknotes the next thing to do would be to standardise the denominations of the bills.
For example 1, 5, 10, 20, 50, 100 and so on. The problem is that unless @Cataphrak can clarify is the composition of the Tierran currency namely is it 90% silver for a Tower and 75% for a Gryphon and the weight of the coin since they should have a standardised weight for each coun respectively. The way a gold backed banknote works is similiar to a modern fiat note except what they do is when someone turns in the note to a bank and ask for its value in gold or silver, they are issued gold and silver from the bank vault worth the amount of the bill.
To change it to a Fiat currency, you remove the whole getting the commodity in exchange for the bill while also ensuring that you maintain control over the silver and gold bulion that your nation holds and would use to back your currency.