In Greece, since November 5 2021, the international permit is no longer necessary for holders of a valid driver's license for motorcycles and passenger cars during their stay in Greece, and whose driver's license was issued by the United States of America or Canada or the United Kingdom or the Commonwealth of America and Gibraltar.
Car rental companies are now fully aware of this text, do not believe anyone who tells you that they are not allowed to rent you a car without an international license
If you are a US citizen and the rental company asks you for an international permit to rent a car, it is in violation of Greek law (article 94 No.4850/2021 paragraph G), who knows what other law they might not respect.
So choose another rental company.