By comfort pad, I'm pretty sure they mean the shoulder pads, not the insert. There would be no way for the insert not to drag the straps down if you were trying to use it with a higher position.
ETA: I reread the manual, and yes, "comfort pads" refers to the shoulder harness covers. The gray insert is called a "head pad."
It says "comfort pad" in the singular and continues w/ the following and a pic of the headpad still in the seat:
Ensure that the harness strap
is not twisted and rethread
the harness strap through the
head pad and then through
the appropriate harness height
slot in the cover and shell
From that I still feel they are talking about the head pad. They do call the harness covers comfort pads later on though so maybe I'm a little unclear about it. What page did you see that it says that it must be removed?