It is believed (mostly by older Greeks) that spitting chases the devil and misfortune away. That is why when someone transfers bad news such as a death or an accident, the people who hear it will usually spit three times. Also, when a Greek person compliments your looks he or she will “spit” on you so that you will be protected from the evil eye, which is called mati in Greek.
However, keep in mind that Greeks don’t literally spit on you but just make a puff of breath through pursed lips, as if spitting. So no, you don’t have to keep a handkerchief with you in case you visit Greece next summer.