Answer me a few questions mate?
Did Greece declare war on Turkey?
Did Greece despatch Naval Warships to attack the Turkish Navy in order to halt the invasion?
Did they despatch fighter aircraft to countenance Turkey's domination of the skies? Did these engage Turkish aircraft?
What percentage of the Armed Forces of the Hellenic Republic fought on Cyprus to defend the island?
Did the Hellenic Armed Forces react in any significant way to defend Cyprus following the invasion; apart from the troops already stationed in Cyprus previously?
The obvious answers to the above questions leads any logical person to the conclusion that Greece did not enter into full-scale warfare to defend Cyprus; which leads me back to my original point. Cyprus cannot obligate Greece to do anything. Greece signs its Treaties out of free will, and once doing so, should uphold them.
Furthermore, the Treaty of Guarantee does not obligate War in any event. If you have ever read the document, you would know this.