The title as prince of Greece and Denmark goes back to 1863, when Prince Vilhelm (Georg I), second eldest son of King Christian IX, was about to be the new King of Greece. His father was well aware that the Greek throne was unstabil, and under normal circumstances, Vilhelm would have to renounce his title as danish prince to become king of Greece. But King Christian made it so, that in case Vilhelm would be disposed, he and his descendants would still be danish princes and princesses, just not in the line to the throne. A way to secure that they had a country where they would be welcome, if they one day should find them selves "countryless".
Prince Phillip renounced his title as prince of Greece and Denmark, when he married QEII, a condition when he gained british citizenship. So Phillip and QEII's children are not princes and princess of Greece and Denmark.