Hello,
It is probably because of the damping factor. It is not ideal to use low impedance headphone with amp with high output impedance. Your headphone is 32Ohm at 1KHz. It is recommended to use headphone amp with output impedance lower than 4Ohm. The FiiO E07K itself have output impedance lower than 1 Ohm. I recommend you to use that for your low impedance headphone or headphone with impedance of lower than 80Ohm. Use the E09K for headphone with impedance higher than 80Ohm.
The reason why you do not find it a problem pairing your Grado with E09K mainly because the Grado have flat impedance vs frequency thus, IMO any output impedance would not affect it much.
Hope it helps,
Billson