Thermocouples - Understanding signal vs. power grounds
The amplifier has a common mode range that goes from slightly (-150mV) below -Vs to some other voltage above ground (the datasheet has an error in it). 

There may be other grounds in the circuit that you are not showing. Often the thermocouple junction is grounded. If not, then it's almost floating with only the 1M resistor taming it. 

Chances are the amplifier common mode range is being exceeded, either from a ground that is not shown or from noise and lack of a ground. 

One thing you can try is to parallel the 1M resistor with a capacitor such as 100nF (and you can reduce that resistor to 10K with little practical effect- T/C circuits are usually &lt;&lt; 100 ohms so even if the junction is grounded it will have no significant effect).