@PhillyBilly
Ah yes, that was the only situation I thought the sword would be useful, letting someone know you absolutely forgave them. Problem, that's incredibly vapid. Forgiveness is an act of restoring trust to someone that has broken it, by necessity, the person forgiving makes the conscious chose to return trust to the person who transgressed, and if the person that transgressed is sincere, they legitimately trust that trust has been restored. By removing this innate concept from the interaction of forgiveness, you've denied the action of all meaning, as it's no longer a social concept, but now a pure statement of fact.
The entire point of the transaction of forgiveness is a social ritual and thus a subjective act. Leaving no room for doubt in the mind of the transgressors robs them of their ability to actually internalize the act of forgiveness. It puts the forgiver in the position of weakness, as opposed to the forgiven, not allowing the later to progress.
Put in a far simpler manner, the one who broke the trust was the Rock Hero, not the Princess, there isn't a concievably non-pathological type of person that gives faux-pardons for people who acted against. The mere act of not executing them should be statement enough, the Princess never broke any trust, it was all on the other party.
The Princess does not strike me as someone to give faux-apologies, I don't think a single person but the most inept would think so. There should be no doubt in their minds if they are forgiven. If anything, all the Princess has committed in acts of lying have been statements of omission and not commission.
As far as "cuts through all defenses" that's thrown around on so many swords across all genres that it's not interesting in the slightest. If we wanted to give Tomboy a sword that ignores defense, just give her the sword that ignores defense, no need to add the "forgiveness" angle.
@strangeirdo
In my scenario, the sword does not check if the Rock Hero has forgiven the Princess, it checks if the Rock Hero is *legitimately remorseful of his actions* towards the princess. This is useful information as he has broken the trust of the Princess he can now lay bare his emotions, and trust would be restored proper. The Princess at no point has broken trust, why would the Rock Hero have reason to doubt her unless he was mentally ill?