Renaissance banking is somewhat beyond my field. But I think you have made the assumption that modern banks and these early banks operated the same way. They did not.

First, the typical bank of, say, 1750 ( like C.Hoares & Co) would be one place, one building, one staff ( often the family) and so one set of ledgers. It would be hard, therefore , to present a check at a branch location- no branches.

But even a big Renaissance banking/merchant house like the Fuggers ( who, like Hoares, started as goldsmiths) with agencies in different cities would not need to have duplicate books at each agency showing all the customers everywhere. If you were a merchant named Fritz in , say Augsberg and you were travelling to Innsbruck and needed 100 ducats, you would go to the Augsberg bank where you'd put your money and get a letter of credit . The Augsberg banker would then write a letter to the Innsbruck bank, saying, give Fritz 100 ducats. There could be a fee for writing the letter. There could also be a discount- the Innsbruck banker might only give you 95 ducats.

So, now it really comes down to the possibility of forgery. This could be hard to do. The two bankers would know of each other and the banks: they might well be cousins or brothers, father and son, and the handwriting would therefore likely be known in Innsbruck- even the handwriting of a company clerk. There would , at some point in time later, be a signature on file that the bankers could consult. For the Renaissance, I would suspect that there would instead be a lot of use made of wax seals, and certainly examples of those would be on hand in Innsbruck, to be consulted. Now, even after all this, someone might be able to duplicate handwriting, duplicate a seal.There were precautions that could be taken against this risk: the note could be greatly discounted, accepted for much less than full face value. Or the note could be held- not accepted until it was proven good. But still, there was a risk, and forgery was severely punished. Even in the 18th c., forgery and counterfeiting were punishable by death in England.

But a bank could be the victim of fraud in other ways. When, later, banks began issuing their own paper money, there was always a chance that someone would take a note in payment without knowing the bank had failed, and be left with a worthless bit of paper. But, in the Renaissance, the big merchant banks like the Fuggers and, before them, the Medici, failed for a different reason. When all those powerful kings, dukes, and princes demanded loans, the bankers had no choice but to make them. The kings, dukes or princes would then often default on the loan, the bankers would be powerless to recoup their losses, and they would have to close their bank.