In That Was Then, This is Now by S.E. Hinton, how is Cathy involved in the separation of Bryon's and Mark's relationship?

Cathy is a part of the emotional change that leads Bryon to distance himself from Mark.
Cathy is a significant part of Bryon's emotional maturation.  She enables him to see beyond the things that used to define him.  Cathy allows Bryon to see that his life of hanging and hustling with Mark, living solely in the moment, and engaging in self-destructive behavior are not ways to live. Cathy encourages Bryon to embrace more sensitive and thought-provoking approaches.  For example, he takes an active role in helping Cathy find her brother.  Bryon displays care and warmth in her time of need.  At the same time, Cathy is instrumental in helping Bryon understand his feelings of regret over Charlie's sacrifice.  She allows him to expand his emotional scope.
Since Mark does not possess such a perspective, Cathy's influence over Bryon facilitates the brothers' separation. Cathy does not intentionally drive a wedge between them. She is not jealous or possessive.  Rather, her goodness is contagious.  It rubs off on Bryon and causes him to ask questions about the person he is and the one he is going to become.  Cathy's effect on Bryon is evident in his betrayal of Mark as he can no longer passively watch what Mark does.  He must take action against it.  Cathy awakens a sense of duty and responsibility in Bryon that Mark lacks.