This is a 2 different cold junction compensated thermocouple smplifier circuit.
These resistors are part of the cold junction compensation, which you need to get an accurate absolute reading. Otherwise the temperature of the cold junction would either need to be temperature stabilized (which was done in the past, using ice baths) or you would get reading that depends on the temperature of your cold junction as well as on the hot junction.
The need for the resistors arise from the temperature coefficient of the diode and the thermocouple being non-linear. These resistors linearise the curve.