Good article, but I wouldn't call that article discussing the 'influence' of islam as much as 'islam's attack of'. The Metropolitan is being kind with words here. What that article walks through is slaughter and subjugation and its lasting effects.

In my mind, influence seems more 'minor' than death or enslavement and would be more about the rise of iconoclasts and the struggle of the early church fighting off that heresy. Also priests wearing a black hat at various times during the liturgy as it harkens back to the Turks requiring the priests identify themselves with a black hat while in public.

Islamic rulers have seldom proved tolerant of Christianity, often saddling them and Jews with jizya, a rather significant extra tax.
And that is when things were at their peaceful best.