They were a galactic power before the Infinite Empire was even a dream is some Rakata's mind. The Republic is crippled and in their debt, the Empire is racked by revolts and defections. Both the Jedi and Sith have been decimated by the Great Galactic War (the Jedi have taken to training Flesh Raiders and Sith while the Sith are training Jedi POWs and slaves they've both become so desperate for bodies). An invasion of the Empire and independent worlds and a Republic that isn't in a position to resist or even complain would make sense if the Gree have gotten patriotic and nogalistic for their glory days.
Have no fear, if they do invade they lose and the Republic rules in hegemony for 3,000 years.
