That's not how an internet forum works.
What you're doing is hijacking someone else's thread.
Hahahaha... I thought that was so funny that I'll try my best to answer the original question even though I typically avoid subjective questions, since as we know, this question is debated back and forth and every imaginable answer is given at one time or another.
But the best way to describe the importance of the GRE is that it varies by school. For instance, on Caltech's website, it lists a strong performance on the Physics GRE as the first item they look for in successful applicants. Other schools officially, or in one way or another, state that the GRE carries very little importance. UPenn is one I've heard of. They're ranked ~20th and have an average GRE of 780 (same as Yale, ~12th) but several schools ranked well below have much higher scores, (Rice for instance, ~32) lists an average of 830. Also, Stanford/Princeton are ranked the same but have averages of 810/880.
As for the question whether the GRE carries more or less importance for women, I don't know. I'd imagine it carries the same relative importance compared to the rest of the app as it does with men.
However, the scores needed for admission may be less. There are plenty of guys out there with a perfect or near perfect GPA who applied to 8 or so REU programs and got accepted to one or none of them. I went to the one that accepted me and met a girl who had a 2.7 GPA and no research experience.
Draw your own conclusions.
But again about the GRE importance, I think it's best to apply to a lot of schools because there's no way to tell, even with statistics, who values what most. It could vary from year to year with who ends up on the admission committee and whatever.
Similar confusion would occur if I dared to ask whether it's better to apply to grad schools with a BA or a BS degree.... If we asked 100 people we'd get a 50-50 split in answers with a wide variety of rationales, none better or worse than any of the others... but no I'm not asking this question, haha...