Rebuilding heater box, replace core?

Tony Barracuda said
Does the small grey foam go anywhere on 67-69 barracuda?
Red arrow.

View attachment 1716123685
Click to expand...
I don't recall at this point but if I didn't mark it I didn't find a use for it.
Longer one goes here
1691337243694.png

This heater boix had been opened before so its not a pristine untouched example.