I have to disagree with [Edit: Some of] the other answers you've gotten. Making greet private and adding a getter does little to increase encapsulation.
Regardless of that, however, I think it's pretty poor OO design. An object should represent some thing (dare I say, some actual obect?) IMO, the "objects" here would really be the people (or whatever), one of whom is greeting the other. The greeting itself should be a message passed from one of those objects to the other. We might write a "greeting" class to hold the text of the greeting, but even if we do the greeting object itself should be independent of the source or target of the greeting.
