Value to me? or to our imaginary 1st-century folk?
But even if someone is not sincere in caring about being forgiven, there is still value in giving forgiveness to them, even if they never knew you forgave them, isn't there?
For the Biblical authors and their contemporaries, no. Forgiveness without recognition is nonsensical, in the same way that "+4^=" is a nonsensical arithmetic statement. In the extreme case, it's obvious that those who do not acknowledge God's forgiving acts are not going to be recipients of his mercy. Hence the parable (of the unforgiving servant)--one way you show your "acknowledgement" is by showing mercy to others.
In the "modern" era, it's easy to confuse "forgiving" (the act) with "forgiveness" (the mood or tendency)*. We don't seem to be able to act without predisposing ourselves (cf Ashton's reference to Jaynes), and we generally prefer the predisposition to the action; another way to say that is, "but he meant well...", or in this case, "I'm really a forgiving person, but circumstances deny me the opportunity to demonstrate that in this particular situation..." We "forgive" then, but not in action, only to soothe our own egos (which obviously need a lot of soothing) in an attempt to maintain a coherent persona** we can live with.
* Thank you very much, Mr. Kant. >:(
** Or, for Ash, if you're reading this, a "meta-actor" a la bicamerality. :)