I do not know if this remains true nowadays, but in the past most Modern Greek speakers pronounced the ancient words with the modern pronunciation, because this is how it was taught in schools, despite the fact that the Ancient Greek pronunciation was very different.

This is the same like with the Latin language used by the Catholic Church, which traditionally had a modern pronunciation very unlike Ancient Latin, or how the Latin was traditionally taught in English schools, also with a modern pronunciation unlike the ancient pronunciation.

In the last half of century, in many places the teaching of ancient languages has switched to using pronunciations as close as possible to what is known about the ancient pronunciations, but I do not know if this has also happened in Greece.

The Modern Greek has replaced many ancient words with more recent loanwords, but as a reaction to this they have created a form of the language, Katharevousa, which was purged from many loanwords and which used a high proportion of Ancient Greek words. Katharevousa was used for many literary works in the past and it was the official language of Greece since independence until 1976. I do not know if there is still much use of Katharevousa for anything, except for reading the older books and other publications that have used it.