I had a history professor who was Greek and she would always refer to this city by its original name before the Ottoman Empire invaded and took the city. Are there still ethnic feuds over the land?
The city was not officially named Istanbul until the 1920s by Attaturk. The Greeks have always called it Constantinople formally (and various other terms informally).
Apparently many ethnic Greeks still refer to Istanbul as Constantinople.
The city's official name in Greek is Κωνσταντινούπολη/Κωνσταντινούπολις and is also often referred just as Η Πόλη / Η Πόλις ("The City"). All Greeks call it like that, rather than just "many" of them them. Greeks never called The City "Istanbul".
a territory that was Greek 550 years ago
The fact that the City wasn't in a Greek dominated state after 1453, doesn't change the fact that hundreds of thousands of Greeks were living there up until 1955 when the Turks pogrommed them after they heard the fake news that Greeks had bombed Kemal's house in Thessalonica, which resulted a mass Greek exodus. Istanbul/Konstantiniyye/etc. was an Ottoman city, which means that it was a multicultural city; it wasn't Turkish in the sense that it is now, up until very recently.
The City is held dearly in almost every Greek's heart. It was the cradle of the Greek people from 323 up until the formation of the Greek state in 1830 and the making of Athens as the capital of Greece in 1834 (which was a village of 4,000 people in 1833).
Are there still ethnic feuds over the land?
The dream of taking the City back stopped being realistic after the 1922 Catastrophe in Asia Minor. Up until then it was one of the main goals (if not The main goal) of the Greeks as a nation.
So, synoptically, the reasons are tradition, history, and the generally very bad Greco-Turkish relations which are still bad even to this day.