As Sverre says, the basic problem here is that the font does not support Greek. Moreover, you are not loading any package to actually deal with multilingual typesetting i.e. either Babel or Polyglossia.
For example, the following works for LuaLaTeX:
\documentclass[11pt,a4paper]{scrartcl}
\usepackage{polyglossia}
\setmainlanguage[variant=british]{english}
\setotherlanguage{greek}
\usepackage{fontspec}
\setmainfont{GFS Artemisia}[Ligatures=TeX]
\newfontfamily\greekfont{GFS Artemisia}[Ligatures=TeX,Script=Greek]
\begin{document}
This is English with some Greek: \textgreek{γέγονεν}.
Isn't that quite nice? εὕρηκα!
\end{document}

The GFS fonts all provide Greek since they are from the Greek Font Society. However, the above example does not work correctly in XeLaTeX.
In contrast, GFS Bodoni works with either XeLaTeX or LuaLaTeX:
\documentclass[11pt,a4paper]{scrartcl}
\usepackage{polyglossia}
\setmainlanguage[variant=british]{english}
\setotherlanguage{greek}
\usepackage{fontspec}
\setmainfont{GFS Bodoni}[Ligatures=TeX]
\newfontfamily\greekfont{GFS Bodoni}[Ligatures=TeX,Script=Greek]
\begin{document}
This is English with some Greek: \textgreek{γέγονεν}.
Isn't that quite nice? εὕρηκα!
\end{document}

You could, of course, still use TeX Gyre Termes as the main font for Latin scripts, but then you need to think about selecting a complementary font for Greek. So if you can find a font you like which supports both Latin and Greek scripts, life is probably easier.
I thought that XITS would make a good alternative to Termes since they are both Times clones. Unfortunately, though, XITS does not give the correct output for either XeLaTeX or LuaLaTeX, so it seems not a good choice, even though it claims to support Greek.
έ(U+03AD). XeLaTeX fakes it somehow, but I don't know how. – Sverre Sep 19 '15 at 15:12