Terry's right. If you could talk to first century Christians and ask them what their "Geeek Sciptures" were, they would produce the Septuagint. That was the "Greek Bible" back then. The term "Hebrew Scriptures" is commonly used outside of the JW world because some people don't want to offend the Jews by calling that portion of the Bible the "Old Testament." It implies it's now longer in force or no longer good any more. So you will hear/see some use of "Hebrew Bible" instead of "Old Testament" outside of JWs, both by Jews and non-Jews.
But the "Christian Greek Scriptures" phrase has got to be another Freddie Franz idosyncrasy, an attempt to distance JWs from "Christendom." I once read that article by George Howard about the tetragrammaton in the New Testament. In it he uses the term "the Greek Bible." He means the Septuagint and the New Testament combined. He does not use the term "Christian Greek Scriptures." That would definitely mark one as JW, but it's not the same as simply saying "Greek Scriptures."