If I had come to the barn and found this, the earth would split and the heavens would fall from the wrath I'd unleash on that girl, the BO, the instructor... There is no reason, no excuse, nothing to justify them using your horse without your consent. It's not their horse. Period. Even if the girl is innocent, I would make a very big deal out of it just to drive home the fact that you will NOT stand for them stepping on your toes and taking advantage of you and your horse.
IMO, you made it worse by passively letting this go and going about your business. This is essentially your silent consent. I would definitely lay it all out for everyone- your horse is NOT a lesson horse and not a single person but the ones you specify should be dealing with him. I would be loud about it so the other boarders and riders knew where you stood, in case they try it again, too. Make it very clear that they're walking a thin line and if you catch even the slightest wiff of them trying anything like this again, you're going to be out of there and it will be at their expense.