Googling "coral kt extinction" gave me this BBC article- https://www.bbc.com/news/science-environment-45133197

So it looks like either corals evolved after the KT extinction event or they survived in very small amounts (maybe a few species) before re-exploding in diversity after the extinction event. This can be seen in global warming today- some corals take to the hotter water better than other corals, and even some regions that have had hotter water historically have corals that aren't really affected, while the Great Barrier Reef and similar are undergoing a mass dying.

EDIT: Also, deep water corals do exist, so it's possible they survived from there. https://en.wikipedia.org/wiki/Deep-water_coral