I saw a post from 2016 that asked this value and didn't get a good enough answer, so I present to you, the gs requirement for Halls of Reflection NM and HC:
Between 4404 and 4499
It unlocks both (NM and HC). I recommend getting gear from the emblem vendors in Dalaran since its pretty easy to get them :)
I understand it's an old thread but please,
stop
involving
gearscore
GEARSCORE IS IRRELEVANT, RDF TOOL DOESN'T CARE ABOUT IT!
It cares only about your average item level, which for Halls of Reflection should be about 219.
The above statement about heirlooms giving 0 gs is false. They do give gs. What they don't give is actual item level, as theirs is 1. So, generally speaking, when you add +1 to your total ilvl and you still devide by 17 or whatever number it is, that one heirloom giving you 1 ilvl is gonna pull the average down and you won't be able to RDF Halls of Reflection.