How is stellar parallax related to the Greeks and the discrediting of the geocentric model?
Greeks didn't have instruments to prove or to discredit the geocentric model by using the stellar parallax.
One of the reasons the old Greeks believed in the geocentric model is because they could not observe stellar parallax. They correctly deduced that if the Earth circled around the Sun, the stars would show parallax around the year. Their error was not knowing the extremely vast distances between us and the other stars. The distances are so big that parallax cannot be perceived by the naked eye. They would need telescopes to observe it.