I do not recall if the insert is removable but I would not remove it anyway in order to maintain the precise alignment of the pins where they meet the contacts on the arm shaft.
The unsoldering/soldering can be done with the insert in place. (I have done that but many years ago.) One should use a small tip iron and tread lightly as these are tiny objects without much heat transfer abilities. Anyone who has ever resoldered on of the cartridge clips to a lead can do it.
Kal