This is the pronunciation used here, and is probably based on the pronunciation used by a Renaissance scholar named Erasmus, who was the main force behind the first printed copies of the Greek New Testament. The Erasmian pronunciation is probably different from the way Greek was pronounced at the time of the New Testament, but it is widespread among scholars, and it has the advantage that every letter is pronounced, which makes it easy to grasp the spelling of words.

This is the way Greek is pronounced today in Greece. Some people prefer to teach this pronunciation for New Testament Greek as well. I initially learned the modern Greek pronunciation, but had difficulty learning to spell words, so I switched to the Erasmian. Modern Greek pronunciation is probably more similar to New Testament Greek pronunciation than Erasmian is, but not identical.

There are some scholarly books which attempt to reconstruct the original pronunciation of New Testament Greek, and they have reached the point that there seems to be fairly widespread agreement on the original pronunciation. As far as I know, nobody ever teaches this pronunciation. Incidentally, since there was a large variety of Greek dialects, there was no single way to pronounce Greek even in the New Testament era.