The one and only Greek royal to marry a Greek woman was King Alexander (reigned 1917-1920) and it was considered morganatic. Although his wife and daughter were raised to the HRH style after his unfortunate early death, I don't think the marriage was ever really approved of by the family, or even by the Greek people.
Nowadays of course the members of the "Greek RF" could marry anyone they choose.
Prince Michael, last surviving grandson of George I, married a Greek woman, Marina Karella. Their daughters are princesses of Greece, but not of Denmark.
Their youngest daughter, Olga, is married to her third cousin Prince Aimone of Savoy-Aosta, Duke of Aosta. The couple has 3 children, 2 boys and 1 girl.
"...Unlike other members of the Greek Royal Family, she was not deemed a full member of the Greek royal house under the monarchy, despite being born of a marriage recognized by King Constantine II of Greece (pursuant to Greek legislative decree 1298/1949). As daughters of a non-dynastic marriage, she and her elder sister, Princess Alexandra, are not accorded the traditional style of Royal Highness, nor do they bear the titular suffix "and Denmark"..."
Marina --> https://en.wikipedia.org/wiki/Marina_Karella
Michael --> https://en.wikipedia.org/...ael_of_Greece_and_Denmark
Michael was a 1st cousin of Philip
Michael is a really fascinating person. If you have not heard of the sad story of Elisa Izquierdo, it's definitely not for the faint of heart, but basically Prince Michael wanted to sponsor a child at a Montessori school in New York and Elisa was chosen. He became close to her and her father offered to pay her tuition through 12th grade, but when her father died, custody was given to her abusive mother. Michael really fought to get her placed with her father's relatives and even when her mother put her in public school, insisted that he was still willing to pay for her private schooling. The story ends, sadly, with tragic results for the little girl. I believe Michael helped pay for her funeral.