To understand it, you first need to understand two of the words in context.
"Cause" has two common meanings.
1) a person or thing that gives rise to an action, phenomenon, or condition.
"the cause of the accident is not clear". source, root, origin, reason, basis, motive
2) a principle, aim, or movement that, because of a deep commitment, one is prepared to defend or advocate.
"she devoted her life to the cause of deaf people" Similar: principle, ideal, belief (in), conviction, tenet, charity, purpose, movement
In this use, it is the second one.
"Just" is used as an adjective. based on or behaving according to what is morally right and fair.
Truth is reality, accurate, exact, in accordance with facts
Damage is harm, impairment, weakening
Reality and facts do not weaken, impair, or harm a principle or belief in that which is moral and righteous.