2003 Toyota Camry transmission

Some transmissions have safeguards built in that prevents a clutch pack from engaging, (shifting into gear), when engine speed is too high. Shifting at that high of speed will shock some of the rotating members. On some designs the fluid must pass through small passages to fill a clutch pack to engage it, and that occurs relatively slowly regardless of engine speed. If the shifts are still crisp and solid, there likely was no damage done.

Not necessarily. I had a tough old Chrysler many years ago that I wanted to shift into neutral to coast down a long hill to a stop sign. I accidentally stuffed it into reverse at 55 mph. That hammered pretty hard on a bushing and it developed a flat spot and a pulsing torque converter vibration, only I didn't know that was the cause until a few years and many miles later when it started dumping fluid on the ground only when the engine stopped running. The vibration pounded on the torque converter's hub until it cracked and broke away. Being the uncommonly reliable car it was, it still got me 80 miles to home after the horrendous banging started.

The way you described what it felt like, I don't think you hurt anything. What is more likely, if anything, is you may have hurried up a future failure. Perhaps the set of clutch plates in one of the clutch packs will start slipping requiring rebuilding the transmission at 245,950 miles instead of not until 269,396 miles.

What are they going to check? The best they can do is test-drive the car and verify it's shifting normally. You can do that. If some related problem shows up in the future, there's no way of predicting that now. Drive the car. Don't fix what's not broken.