3D printer thermocouple noise issues
If you have a reference junction then you could use a scheme like this.



If it's high frequency noise (+100Mhz rectifying at the amplifier) you might want to try simply adding a clamp on ferrite on the cable or wrapping the thermocouple cable a few times around a ferrite core if you have one lying around. Make sure the thermocouple wire is not making a loop and twist it if its long. 

Another option would be to filter the output of the MAX6675 and add a passive or active low pass filter