Greece tour that’s starts April 2,2022. Do we need to be Covid tested?

For entry to Greece, no, you should not, but check with your airline, it can depend on where you are going through as wel to get to Greece.

Separate from that, your tour may require a test, check with the tour operator.

An edit: Regardless of requirements, each time I have gotten on an International flight, I have at least taken a self-test, just common sense and respectful of others.

Are you referring to a Rick Steves tour? If yes, there is a link in your online tour account labeled ‘view tour itinerary’ which may have the information you seek (mine does). If additional questions regarding any tour requirements, best to reach out to the Rick Steves tour office directly by email or phone.

If you are vaccinated and can show proof (the us cdc card counts) you don’t need to be tested to enter Greece

https://travel.gov.gr/#/ Is the Greek government site with the rules.

Your tour may require a test, I don’t know. And you need a test taken 1 day before your flight home to get back into the US.

Please note that the measures indicated at https://travel.gov.gr/#/ are valid until April 4.
They may be different from April 5.