Can a grounded thermocouple cause GFCI to trip?
I understand the GFCI compares voltages and trips if there is a difference (in the millivolt range).


Actually, the GFCI compares current (in the "line" and "neutral" wires) and trips if there's a difference of more than a few mA.


  If the thermocouple generates a small amount of voltage, can't it trip the GCFI?


No, the thermocouple (if your iron even has one) would be unrelated to this.


  Moreover, what does the GFCI use as a voltage reference?


A GFCI does not need a great deal of precision, so it probably just uses a diode junction as a voltage reference.