My daughter drove her pickup in 3rd gear on the highway. Will it damage the transmission?
Probably not. The engine is going to be running faster than normal to make highway speeds in 3rd, if she got going fast enough it was probably pretty loud. Depending on the vehicle there may be a rev limiter to prevent the engine from running at too high a speed. Teach her to hear what the truck sounds like when it is time to shift if you can.
Most contributing writers are probably aware of this, but readers may not be.
The actual answer depends upon the final transmission output gear ratio. If fourth is an overdrive gear (less than 1:1, say 0.7:1), it is fine to drive in 3rd and even recommended in some situations to improve driving experience and vehicle performance (examples - stop and go traffic, towing).
But if it is a transmission that does not have an overdrive gear or overdrive is a gear greater than 4th (fourth gear trans final output ratio is 1:1 or greater), then driving in third is not recommended; although, as stated, it can be done with usually minor consequences (higher trans temperatures, greater engine wear, decreased fuel economy, and slightly greater chance of engine failure). Results vary.