For some reason, I started thinking of JSA Classified #1, which was the storyarc Conner, Johns, and Palmiotti did which was supposed to explain how Power Girl's origin worked after Crisis on the Infinite Earths erased Earth-2. In reality, I don't think it did that (or rather I didn't see how reiterating she was from an Earth that had been made to never exist explained anything), but whatever.
I was thinking specifically of a scene from the first issue where Peej sees a boy in danger and bursts through the window of her apartment to make the save. She's reflecting on how bad she is at maintaining a secret identity, and recalls a conversation with Green Lantern. GL asked why she didn't wear a mask, she replied most people weren't looking at her face (and indeed the boy is gawking at her chest, as she tries to get him to redirect his gaze up and acknowledge the person who just saved his life).
So which Green Lantern was it?
I couldn't find the page anywhere, but I'm pretty sure Power Girl referred to the Lantern as "him", so rule out Jade, though she didn't wear a mask either, so she probably wouldn't ask. Those both rule out those alien Green Lanterns that stayed on Earth for awhile (Kilowog, Salaak, Katma, Arisa), so I figure we're down to the Earth boys. John doesn't have a mask, so I don't see him asking. Neither does Guy, though my guess is he'd be too busy leering or making an inappropriate comment to ask anyway. I can't see Peej being that flip if Alan Scott asked her.
Which leaves Hal or Kyle.
Hal's the most likely choice. For one, this is a Geoff Johns written story, he's going to default to Hal almost without fail. For another, Hal actually was on a team with Power Girl for awhile, and they were even close for a bit, I think (which is really poor judgment on her part, but let's chalk it up to all the origin confusion messing with her). I kind of see Hal not caring enough to ask. He worked with Black Canary, she never wore a mask, though I guess she had a wig some of the time. Wonder Woman doesn't wear a mask, neither does Superman. His best friend (or second-best, maybe Barry was his best buddy) Oliver Queen wears a mask, but everyone seemed to know who he was anyway. Hal probably wouldn't think anything of another hero not wearing a mask.
At the same time, Kyle strikes me as the one who would be more concerned about secret identities, even though he was absolutely terrible at maintaining his (hey, something they have in common!) Kyle unfortunately got a graphic lesson early on about what happens when bad guys know who you are in your off-hours. Not that Power Girl needs to worry about a dweeb like Major Force, or that she has many non-powered friends to worry about (especially back when this comic was written), but Kyle might not know that, and you can see why it might weigh on his mind. He's fought alongside a lot of those same heroes Hal did, but you know how Kyle for a long time felt out of place among them, so I think he'd have a hard time approaching Superman about it*. Power Girl might seem less intimidating, strange as that sounds, given the fact she can be a bit more prickly than Supes.
* I can't remember, in that story Mark Waid did, where the JLA split into two people, one their superhero identities, the other their civilian, did Kyle reveal he didn't think Superman even had a secret identity when he learned it? Or was that Batman?