After some digging, article 8 of the bilateral trade agreement between Greece and the United States, states that:
Students or business apprentices who are residents of one of the Contracting States but who
are temporarily present in the other Contracting State exclusively for the purposes of study or for
acquiring business experience shall not be taxable by such other Contracting State upon
remittances received by them from sources without such other State for the purpose of their
maintenance or studies.
If I am understanding this correctly, insofar as my part-time work is used to maintain myself during my studies, it is not taxable within Greece.
