There are a variety of reasons the car can enter limp-home mode, all of them having to do with the electronic throttle not being able to function properly. The computer does this to prevent any sort of uncontrolled acceleration that could lead to losing control of the vehicle.
Presuming the dealer received a code indicating a problem with the accelerator position sensor, replacing the accelerator pedal assembly, which contains the sensor, would be the typical repair. Presuming the same code returns, we've either got a defective or incorrect replacement part, a problem in the circuit between the pedal and the PCM, or a problem with the PCM itself.
Typically, when this issue arises, the readings are again correct by the time the car reaches the dealer, usually reducing the technician to making an educated guess from the data stored by the PCM.
According to the people I've talked to at Hyundai, the problem is usually the accelerator pedal assembly (again, presuming a trouble code for the accelerator position sensor), but they've also seen issues with the harness connector for the pedal assembly as well as the harness connector for the PCM.
A last idea that I have stuck in the back of my head is that the diagnostic tool's description of the trouble codes makes unclear whether the problem was with the accelerator position sensor (on pedal) readings or the throttle position sensor (on throttle body) readings. Hyundai has issued TSBs to clarify this, but there's no guarantee the technican knows about these or bothered to look. Does any of your paperwork indicate the trouble codes retrieved from the PCM?
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