Actually, the country didn't want to open its borders to tourists again until May 14th.
Greece would like to welcome tourists sooner: Despite the high number of new corona infections, the quarantine obligation is to be abolished next week. That reports among other things Travel before 9. The government wants to gradually lift the restrictions from next week, before the full opening on May 14th.
Among other things, visitors from EU member states and four other countries should be allowed to re-enter via the airports of Athens, Thessaloniki, Heraklion, Chania, Rhodes, Kos, Mykonos, Santorini and Corfu. The only requirement mentioned here is the presentation of a negative PCR test that is not more than 72 hours old. So far, all travelers from abroad have to be in quarantine for seven days.