Using a terminal block like that means that the actual cold junction temperature is the temperature of the terminal block/thermocouple wire junctions.
To the extent your cold junction temperature sensor does not measure that temperature accurately you will have additional errors. To the extent the different varies you will have noise/drift in the measurement.
So your goal, being stuck with an inconvenient semiconductor package, is to get the chip as close to the terminal block as practical and to make sure that all the items are as isothermal as necessary to meet your target specifications for accuracy and drift.
It's not unusual to get differences of a few °C here and there, and they may change significantly as your circuit warms up and heat is conducted in and out of the enclosure.
Your Molex connector will have similar problems. The female spring part will have less thermal coupling to the pin and PCB than a terminal block, so it will likely be more prone to errors due to heat flowing down the T/C wires. On top of that, it is a crimped type. With a very good crimping tool you may be able to get reliable gas-tight joints but it's certainly a possible source of issues. With a bad crimp problems over time are almost guaranteed. For very good metallurgical reasons, popular thermocouple materials are somewhat difficult to reliably connect to without something like welding.