Insurance from Greek car rental companies or from my credit card?

First check to see if your CC covers car rentals in Greece, and if so, what exclusions there are.

As CJean mentioned, some credit cards will be responsible for certain damages for rental cars, but you must decline the rental company's coverage.

It would help to know what credit card you have. For example, I have a Chase Sapphire Preferred card, as well as an AMEX Delta Skymiles card, and both of those cover the collision damage waiver (aka loss damage waiver). But not all cards do. If you're not sure, it's better to pay the rental car company.

Here is an article that explains it pretty well. https://www.nerdwallet.com/article/credit-cards/credit-card-rental-car-coverage

The potential problem with relying on your credit card company's rental insurance is that you will still be charged by the rental company for the damage and it will be up to you to file a claim with your CC company for reimbursement, and that's IF your coverage covers the reported damage. And we know just how happy and willing that insurance underwriters are to pay claims! You're better off paying extra to the rental company for their added coverage and let them deal with their own underwriter at their own convenience.

Thank you!