To _fix up_ idiomatically means to improve or repair. From the Merriam-Webster Dictionary entry for **fix up** :
> _transitive verb_
> 1: refurbish
> _fix up_ the attic
Holden is thinking about how undertakers _fix up_ or refurbish corpses. Specifically, they perform cosmetic repairs to any damage to the corpse's facial features from injuries that might have been the cause of death; dress the corpse up in formal clothes; style the corpse's hair; and apply makeup to make the deceased look as good as possible.
Holden sees this as another example of the hypocrisy that finds all-pervading in the universe. According to our hero, everything and everybody in the world is "phony", and the general practice of fixing up a corpse to look good when it is, after all, _**dead**_ is part of this lack of authenticity. For Holden, fixing up a corpse to mask incipient decay shows how in this phony world, appearance matters more than reality.