Do Tourists Need a Codice Fiscale in Italy for Bookings and Refunds?

No you don’t need it. There’s no practical way for you to get one and I have never needed to provide that or my SS# as a tourist. You’ll typically need passport info but that’s it.

Wondering what kind of service are you using. As an Italian I have my codice fiscale, it is absolutely necessary for financial or health services (the codice fiscale card doubles as national health card), you may be asked for high value purchases (say, gold coins), it is necessary if you are invoicing anybody, but but for these cases I do not remember using the codice.

There is no way to get one (social security number for Italians) since you don’t live in Italy and are a visiting tourist . (My daughter was born in Italy so she has one but as non Italian parents we never did)
Just make sure you didn’t enter the web site as a non American by mistake . Also - were you born abroad? When I enter my daughter’s birthplace of Italy I sometimes get asked extra info even though she is an American citizen.

The codice fiscale simply encodes some letters of your name, your birth place and date and sticks a control code on the end. You can actually compute an unofficial code online as there is no mystery about it, even if for real work you should better have an official one (in issuing your official code, the revenue agency checks for duplicates that are rare for Italians, but relatively frequent for foreigners, where entire countries are classified under a single short code).

A foreigner can ask for a code and it will be required for most financial operations, I actually have asked the revenue service to assign codes to foreigners that had issued invoices involving Italian taxes to be withhold at source. But you get a tax card, that entitles you to health services, only if you are a resident (not necessarily an Italian).