The clips just hold the housing halves together and the core stays connected to the heater hoses.
That job is a lot easier if you just take the heater out.
You might find like I did that you might want to redo some of the foam on the doors inside there while it's opened up.
4 bolts under the hood around the blower motor, the J hook inside the right vent door, a wire or two and the control cables along with the defroster hoses and it's out.
View attachment 1715164595
View attachment 1715164596