Hey Karl,
The trial extension is not a product key, yet the user is entering the extension into the product key entry box.
The TA wizard version 3.0 and newer has the trial extension entry built right into the wizard (so you don't have to build your own). However, this entry box is only visible when the trial has already expired. You'll see an "Other options" button on the start screen in the wizard. Then they can click "Extend trial" and paste their trial extension in.
If this is a paying customer they should be using product keys and activating your software. Trial extensions aren't "hardware-locked", meaning they can be used over and over again. Product keys are hardware-locked, meaning you can control exactly how many times the key can be used.
Does this make sense?