How does Winston make use of the INGSOC idea of "the mutability of the past" as he deals with Comrade Withers and Comrade Ogilvy? The basic idea of...

The answer can
be found in Part I, Chapter 4 of :

In
the speech under review, Big Brother had referred to an organization called the FFCC, praised it
and singled out an official, Withers, for special commendation. Now
the organization no longer existed and Withers was an unperson.
No one usually knew what happened to those declared as unpersons, public executions or trials
of political offenders were spectacles which happened only once every two years or so. Usually
such people just disappeared.
Nowhad to rewrite Big Brothers speech without any
reference to FFCC or Withers. He decides to invent a totally new person as the subject of the
speech and names this imaginary character Comrade Oglivy. Of
course, Comrade Oglivy did not exist, but once Big Brothers speech
about him was placed in the newspapers with a couple of faked photographs his existence would
become indisputable fact. Winston writes the speech in which Big Brother pays glowing tribute to
the heroic life and glorious death of Comrade Oglivy who is held up
as an example for all citizens to follow.

The fate of
these two foreshadows what will happen to Winston and : by the end of the novel they too will
become unpersons.  The Party will falsify their past written records so that it appears--on
paper--that they never existed.

The "mutability of the past" shows
that the Party is a well-oiled machine of censorship and disinformation.  Since they control all
newspaper and language in the Ministry of Truth, the Outer Party and Proles believe their
propaganda.  Winston's job, after all, is to erase names and pictures of party dissidents.  The
Party's ability to change history and language enables them to torture and dis-inform, and it
strengthens their control over the masses, making it nearly impossible to organize and
rebel.