International Driving Permit

It's not a legal requirement for the rental company to ask you, but it is the law to have one to drive in Italy. Being pulled over by the police is what you should be concerned about. A coworker had a flat tire in Italy recently and the police pulled over to help, and they also asked for his license and IDP. I believe their was a post earlier this year about someone going to a lawyer in Rome to get their license notarized in lieu of an IDP which is only available from your home country.

It isn't the rental company. they may or may not want to see it. If they want to deny you the car for some reason then it would be an excuse to do so, but they don't routinely ask. BUT the only time we were stopped by police, it was the first thing they asked for -- and they seemed a bit disappointed that we had it since it looked like they were girding up to rant at us. If you get in an accident it might void your insurance to not have it and you will certainly be asked for it then. It is cheap and easy to get. It is ridiculous that it needs to be renewed each year -- but it is easy.

Past discussion on same problem

https://community.ricksteves.com/travel-forum/italy/international-drivers-license-86ee77ae-0270-40da-9146-4a5106ec3f80

Update: We ended up hiring a lawyer in Rome to translate our Drivers License and then proceed to go to court on our behalf for the official stamp of approval. We went to the US embassy website and they provide a list of lawyers. We went with the first option and on her website she specifically outlines what to do and expect for this service. We emailed her photos of our Drivers license, payed her about 160.00 USD and we had our documents the next day. We met her in the city to pick up the originals but she said many of her clients are fine with a scan of the documents and she keeps the originals. It was an easy process and I am grateful to all of you for your input.

What the party in your circumstance did ( from the post above by Christine)

As you're now in Italy, you won't be able to obtain an IDP. Those are obtained at any AAA office for a small fee, but must be obtained before you leave home. Whether the rental agency asks to see it or not, it IS the law for visitors to have an IDP. If you have any interactions with police and can't produce one, you may end up with a hefty fine! Roberto has posted the applicable sections of the law in the past, but I doubt that I'd be able to find them on the forum.

Based on what others have posted about getting a lawyer to provide a translation of your license, that seems like your best option under the circumstances.

The sworn translation is your only option if you are in Italy already. In the post by Christine I gave some links I found online.
The law has t changed. The IDP is required by art. 135 of the Italian vehicle code. Driving without one carries a minimum fine of 408€. I’ve never been asked for one by a rental agency, although some do, so SicilyByCar may not and rent you a car without it, but the issue is if you get pulled over. Routine checks at road blocks by police or Carabinieri are very common in Italy, and you don’t need to violate any traffic laws for them to stop you. I was pulled over by the Carabinieri at a road block Fod knows how many times, including last month, for no reason other than they were bored and they needed to justify their pay. They asked for my documents, including passport, California driver’s license and IDP, and after checking my personal record and the rental car’s papers with their central station (Italian cars need to have a full mechanical check by an authorized check station every two years), they let me go on my merry way.