The purpose of this 1MΩ resistor is, that any bias/offset currents that may be
flowing create a common-mode voltage through the 1MΩ resistor and that
common-mode voltage will be rejected by the amplifier.
Additionally if there is no electrical connection at the measurement junction
(insulated tip), the resistor is small enough so that no meaningful common-mode
voltage is generated. If there is an electrical connection through a grounded
or exposed tip, the resistor value is large enough so that any current from the
measurement tip to ground is very small, preventing measurement errors.
We have also more discussion of thermocouple grounding in video form, as a
whiteboard series: https://www.youtube.com/Thermocouple