It was nice of the Avatar to offer to teach her airbending. His motives may have been questionable (Azula can't remember playing a game without doing everything to win but she'd willingly lose at the "air scooter championship" if only for peace of mind), but it was still nice of him to offer.
Azula had made fixes to the Avatar's firebending form in return, really Zuko when will you master the basics, but the changes she made for him were small in comparison to teaching her a century forgotten bending style.
It was starting to feel like pity.
So when Azula saw his eyes linger on the marks on her hands, she had thought nothing of showing him the full mark except that it would make them even.
In hindsight, disrobing without warning had been less than wise. If the red on his face was anything to go by, Air Nomads must not see a lot of shirtless women. Still, it's not as though she wasn't wearing anything underneath.
The mark was only on her arms and across her shoulders, the most risque part was her neck, so she didn't see any reason not to let the Avatar touch her mark. Especially when he pointed out that hers didn't appear to follow her chi path and was more of a decorative marking along her bones.
The chances of her chi path changing was a possibility that verged from the improbable to the impossible. Azula would have been the first to know if her chi path had changed, after all, but when the Avatar offered to check she was far too amused to decline.
Firebenders can draw heat along their chi path. If her chi path has changed, which she sincerely doubted it had, the Avatar would be able to tell by pressing his fingers and feeling the temperature of her body.
Of course, he would only feel around her mark. Which, again, was only on her arms and across her shoulders.
It was innocent.
That still didn't stop the waterbender from screaming.
