I suspect there's room here for an interesting discussion of what a person should or should not say in response to an accusation, true or not. A person's reputation is worth preserving, though lying seems like a bad way to protect it.
That's a question I've never thought about before. The Catechism states:
Honor is the social witness given to human dignity, and everyone enjoys a natural right to the honor of his name and reputation and to respect.
If the honor of one's reputation is a natural right, does that make preserving one's reputation something to be sought for its own sake? If there is an "objectively valid reason" to disclose "another's faults and failings to persons who did not know them" (the Catechism defines detraction as such disclosure when there is no such reason) -- if, in other words, my reputation is justly injured, what natural right to my reputation and to respect do I still possess?
My inclination is to think the Christian's interest in the social witness to his human dignity ought to be selfless. He should defend his reputation not so much for his own sake as for the sake of others.
He has a duty to provide for himself (and his family, if any), and so to that extent should be concerned about how injuries to his reputation affect his ability to provide for himself.
In addition, he should protect and preserve his reputation insofar as doing so helps others who might otherwise be similarly unjustly harmed. If I insist society bears witness to my human dignity, I am also (at least implicitly) insisting witness be borne to everyone's human dignity. How people treat me teaches them how others may be treated.
Finally, Christians are commissioned disciples of Christ. We are to make disciples of all nations, to carry the Good News of Jesus Christ, the Son of God, to all creatures. As a disciple, I should be concerned with my reputation to the extent it helps me make disciples of others, and only to that extent.
St. Paul can sound a little huffy on the point that he worked for a living while preaching among the churches he founded, even though the churches should have been willing to support him. His concern, though, isn't that the Thessalonians admire him for being such a hard worker, but that they imitate him as a servant of Christ.
So too, I shouldn't care if my reputation suffers but my ability to give witness to Christ does not. We are called to put all of ourselves into the service of Christ, and what cannot be put to such service is of no great value.