It's a dead key, right? So just press that key like normal, and then the letter it's supposed to modify. Pressing the dead key will not print anything to the screen.
For example, on the UK QWERTY layout with dead keys, you press the ` key and nothing shows up, but when you press e directly after, you get è. Surely the Greek layout is similar. I don't use the input method switcher in that preferences pane. It only lets me select four input methods, and I always have at least 5. Because of this, I use IBus directly, and have the IBus input switcher in my panel. I have 18 right now. IBus doesn't seem to have the layout you were talking about. 1. Arabic 2. Chinese 3. UK Dvorak 4. UK QWERTY 5. Esperanto 6. German 7. Greek, Modern (the only other option is "Greek, Ancient". I don't see "Polytonic" anywhere.) 8. Hebrew 9. Phoenician 10. Hindi (inscript) 11. Japanese 12. International Phonetic Alphabet 13. Math (LaTeX) 14. Input raw Unicode number 15. Emoji 16. Russian 17. Spanish 18. Yiddish (YIVO) IBus input methods are fairly easy to make. I made #9 Phoenician for writing paleo-Hebrew text, and it works very well. It corresponds to the Israeli keyboard layout. http://www.studymongolian.net/technical/how-to-create-linux-input-metho d-editor/ (I use Phoenician letters as a workaround, because my SMS service JMP's carrier blocks all messages containing Hebrew letters. Luckily, my Hebrew-speaking friends can read the ancient Hebrew script.)