In "Rules of the Game", Carmen reveals that Even Evil Has Standards when she tries to rescue a falling Ivy. Persisting even as Ivy resists.
Carmen: Don't be childish! I'm trying to save you.
And even after Ivy realizes that she's better off accepting the help than not, she can't manage to maintain her grip. As she falls, you can actually hear the concern in Carmen's voice as she calls out to Ivy.
After Carmen steals the orphanage she once called home, Zack and Ivy decide to leave her be, as it was the only home that Carmen had ever known, and it was scheduled for demolition the next day anyway.
After Carmen eludes every ACME Detective at once, the detectives find that she left them all Christmas gifts. Each turns out to be a doll that teases that it is the only Carmen that they would ever catch, and wishes a Merry Christmas. Cue Ivy looking wistfully over her shoulder and whispering, "Merry Christmas, Carmen."
And the whole reason Carmen had Manny "kidnap" the Chief? To play chess like they did every Christmas when she was an ACME agent. Not to mention her growing concern for the Chief suffering a viral malfunction and not wanting to lose him; if nothing, it cements Carmen as a Thief With A Heart Of Gold who still cares for her former partner.
While playing matchmaker was mostly to aid Carmen in distracting the detectives from her true objective, after Ivy and Josha have a date together, Carmen tells the player that she did enjoy playing cupid.