Many ancient greek texts were meticulously copied by monks in medieval times, it was seen as a form of meditation and art. That being said the fire which razed the Library of Alexandria was true tragedy for human civilization as a vast plethora of the most respected epoch anyways. Much the same as it is today, but we have the benefit of modern science and archeology.

The problem with writing things down on papyrus was that it just couldn't last through the ages so a good majority of what was documented by the ancients is just simply unknown.

As for the Renaissance I'm not certain as to what role the ancient Greek culture had on it. But it is easy to see the Renaissance romanticized and admired the ancient Greeks during the Renaissance. Art, sculptures, mathematical equations, philosophy etc... To answer the question, it was more than likely the church and more specifically the monks who had the access to the ancient Greek texts. Which were Byzantine copies of Roman copies of ancient Greek originals. But as I said, it was a tiny snapshot of what actually was.