How can I tell from a datasheet if a thermocouple amplifier IC will work with a grounded thermocouple?
Typically you look for this (MAXIM part): -

Input Common-Mode Range 0.5 to 1.4 V


It doesn't go down to (or below) 0 volts hence it's no good for a ground connected TC.

The AD part says this: -

Input Voltage Range −VS – 0.2 to  +VS – 1.6


And this would be suitable to go 0.2 volts below the negative rail on the chip.

And for the LT part it says a similar story: -

Common Mode Input Range  –0.05 to VDD – 0.3


So you have: -


Input Common-Mode Range
Input Voltage Range
Common Mode Input Range


As the main phrases to look for when choosing a chip that can handle grounded TC inputs.