Actually, :middle_finger : was a default emoji of Discourse, the platform the boards are hosted on . The TTV crew replaced it with Greg as a funny way of censoring it. Shortly after the reactions were first introduced, Greg was included as one of the reactions by popular demand. Often people will use it on posts relating to Galidor in some way, or as Monarth said, on posts with a good lore or story.
Or, like the hamburger reaction, it can simply be whatever. Up to you.