A standard answer is that if the girl is having a good time, even if she knows you're gaming her, she'll go along with it. So it doesn't matter and would generally come up with girls you weren't going to get anyway. I agree. (It's a bit like magicians doing magic tricks with audience assistants – usually the assistant will try to be helpful, not disrupt the act, even if he or she catches something the magician did.)
You can also just treat it as any other shit test and pass it. No big deal. This isn't the sort of thing that guys worry about if they're great PUAs.
I have another answer which I haven't seen. It won't work for everyone, but it will work for many people who ask this question. It works best for intellectuals and the kind of people who don't like game tricks and feel a little bad about using them (who are the same guys worrying about being caught).
So think about it this way. You used a game trick, e.g. a canned line. You didn't feel quite right about it. You weren't thrilled with it. You sorta wish the world was different and it was easier to get girls without learning PUA. If you feel that way, you may also worry: what if she recognizes it's a canned line? What if she calls me on it?
Well, if she calls you out on using the thing you had mixed feelings about, she is exactly the kind of girl you were looking for. She's smart, or she's honest, or reads PUA, or she's bold, or some other good traits. You should be fucking thrilled. Smile. Grin. Confess, happily. Tell her you're so glad she noticed, and now you really like her. Praise her for being logical, noticing details, being knowledgeable, or whatever fits the specific situation. Tell her how hard it is to find a girl like her. Say you were always hoping someone would call you on it instead of falling for the line. Tell her you now believe the two of you will get along great.
If you don't like something, and she doesn't like it, that's great. You have something in common. You see through a lot of social games, and so does she – perfect! You're the more honest type, and so is she – compatibility! (To be clear, a lot of PUA isn't any kind of trick and there's nothing wrong with it. And especially skillful PUAs don't need training wheels like canned openers. It's possible to do PUA honestly.)
This is a very powerful reframing of the situation. It turns a negative into a positive. And it's true, isn't it? OK not for all guys, but something like this is true for a lot of the guys who had this worry.
If you frame the situation as two people who prefer honesty finding each other, as this wonderful, rare meeting, then the part where you got caught is this tiny little detail to be forgotten. It just doesn't matter anymore and doesn't get in the way of the exciting new possibilities you have together.
PUA teaches – correctly – to find something you like about a girl other than her sex appeal and clearly communicate that you appreciate that about her. It's a major concept called 'qualifying'. You get her to express some trait or value she has, and then you are able to give her actual reasons that you like her which she'll be happy with. (Some PUAs lie and say you like whatever her qualities are, but it's better for everyone if you find someone you're more compatible with. And if you have an abundance mentality where you know you can get someone else who fits you better, you'll do better with girls anyway.)
And yes you still have to calibrate. If she doesn't start smiling back, you can't gush quite that much. But something like that can be your natural, congruent reaction to being caught. If you mean it, you can draw her in to that frame, that narrative, that perspective. It's the default starting place, and then you calibrate a bit from there, as always.
(Calibration is not a dirty trick, it just consists of noticing if you and she aren't on the same page. If you're not on the same page, you adjust and try to fix it, or decide you're incompatible and part ways, but you don't just keep talking past her. That's logical. The main hard part of calibration is that some of her signals are nonverbal, so you might misread them and calibrate wrong. There's nothing dishonest about improving at understanding nonverbal communication.)
PS If you're perfectly happy to lie for sex, and get caught using PUA tricks, just lie that you were looking for a smart girl who sees through those tricks. Just do the above as an act if you want. Shrug.
Update: Disclaimer: this is a post about PUA. If you want to do or understand PUA, you can learn something. This is not advice. My recommendation for your lifestyle is: learn philosophy instead of getting involved in stereotyped relationships.