Tax: The US keeps its claim on you
US citizens abroad generally file as they would at home, on worldwide income. The 1950 convention lets each country tax its own citizens as if the convention did not exist, so it does not take you out of US tax; Greece gives credit for US tax on income from US sources, and the US allows a credit for Greek tax.
More detail
Private pensions paid from one country to a resident of the other are exempt in the paying country under article XI, but the same saving clause lets the US tax its citizens. The 2026 exclusion limit is $132,900, and you cannot take a foreign tax credit on income you exclude. Foreign accounts above $10,000 in total at any time in the year are reportable on an FBAR. The convention dates from 1950 and covers income tax; it is not a social security agreement.
Sources: Internal Revenue Service, Financial Crimes Enforcement Network (FinCEN). Checked 15 October 2026.