According to the official announcement of the Consulate of Greece in the U.K., holding a Schengen visa does not automatically entitle you to enter the Schengen area. The process to grant a Schengen visa is unrelated to the border restrictions on travel from third countries to protect against the COVID-19 pandemic. Consequently, third-country nationals (U.S.A., U.A.E, Russian Federation, Serbia, Israel, the U.K.), for whom other EU Member States and countries that belong to the Schengen area apply restrictions at the borders, may enter the Greek territory ONLY with direct flights or with flights through third countries (provided that their entry in the third countries has been secured).
1. Although according to the EU guidelines third-country nationals, regardless of their nationality, travelling through the EU+ (transit) must be able to travel through and have a reasonable / realistic transit time (an overnight may be required), in practice, problems arise for the third-country nationals at intermediate stops (cancellations, revocations).
2. As per the European Commission’s latest announcements, there are no new regulations due to the pandemic and the “Visa Code” is still in force. In addition to that, Member States have been advised to proceed with the issuance of Schengen visas so as to avoid the creation of a large volume of pending applications upon returning to normalcy.