XTR Harmonic Exciter

In the early 1980s a company called XTR marketed an unconventional harmonic exciter. The purpose of this device was to cancel the harmonic distortion that occurs in umpteenth-generation analogue tape recordings. This was done by adding equal, but opposite, harmonic distortion to the audio signal.

Is it true that the harmonic distortion in analogue tape only contains odd-ordered harmonics?

The percentage of harmonic distortion in analogue tape increases as the signal gets louder. I suspect that the transfer function for this behavior is something like the transfer function for the behavior of a spring.