Hard to know more without specifics, but your best option is probably to pay and then consider making an appeal within the allowed amount of time. It usually doesn't work but not paying and just appealing is not a good option. Italian traffic fines are doubled when you pay late, and they'll often go after you aggressively using a collection agency.

This is one of the downsides of renting a car in Italy as opposed to taking the train, unless you are just going to roam around the countryside. I've heard of people coming back with 4-5 tickets accumulated during one day from doing things like crossing a buses only lane, driving in ZTL, etc., and not receiving the ticket until almost a year later. It's easy to drive in Italy, but with some prior research on do's and don'ts is in order.

Unlike the USA where you can drink, drive, speed, and usually without much consequence, Italy is stringent about its driving laws. Velovex cameras are all over, and there are usually large signs written in Italian telling you that you are approaching one. This is because they are not trying to rip off tourists. They want you to slow down and be safe. Italy may be more strict than the USA but it is considerably more lenient than many other european countries. I've heard that in Norway fines for speeding are 10% of your yearly income, and are as high as $2700 in Iceland. Europe is different.

There are cameras called Autovelox all over Italy that record your speed and send you a ticket. You don't need a policeman with a radar gun. I can tell you that your thought of not paying and just sending an appeal letter pleading ignorance or misunderstanding is as unlikely to work as it is in the USA.

If you tell a police officer here that you didn't know that this was actually a school zone, they will say that, ignorance is no defense. I sympathize with you that the letter may have been mistranslated or not clear, but that won't work because they won't perceive it as their fault if you didn't understand them in their country.

If you don't pay, or if you just appeal that you made a mistake and they throw out the appeal, they will just double the fine. If you rented a car they will charge it to your card and add another 50 euro administration fee for having to transfer the funds through the card. Then the credit card company comes after you. Some people do get away with not paying Italian tickets when they return to the USA, but I can't say that's a regular experience. I'm really sorry this happened to you. Hopefully others take this into account.