Ok...so I was up for a challenge. I have no knowledge of Greek; but, hey, why not?
I read the inscription as: Μετ αγωνα Τα αθγα.
My Google-fu skills came up with variations of the following: "Round the struggle ______"
"
Μετ" = Round or " Μετ’ " (with the accent mark) = Return
"
αγωνα" = I found through trial and error that the word "αγωνα" can mean: struggle, fight, race, match, challenge, bout, etc.
"
Τα" = the
"
αθγα" = athga (I don't know what this is)
HOWEVER.....
University of Trinity College in Toronto has the motto "Μετ’ Ἀγῶνα Στέφανος" or "Met' agona stephanos", which means "After Struggle, There is a Crown". That's the same way the inscription on the pin is spelling the first two words. Also, if I take the inscription on the badge and move that first "a" letter over to spell "Μετα γωνα..." that also translates as "After struggle...."
SO.....my uneducated guess is that the inscription reads "After struggle, the ______". I don't know what that last word is.
Edited to add: The second to last letter could also be an "N" and not a "G". If so, it's one letter off from spelling the word "Athens". In that case, "After the race to Athens" might also be a workable motto.