Which version to use? Neither! This is one of those contexts1 where most native speakers would feel they have to use the Past Perfect...
Hi, I'm sorry, I hadn't seen your letter. I've just found it. How are you?
Present Perfect (I haven't seen it) doesn't make sense here, because that always implies from the Past up to and including the Present. Which clearly can't be correct, since the speaker goes on to say I've just found it.
The only way it could make sense with Present Perfect would be if we assume the speaker meant he hadn't actually read the letter (even though he's seen it, so knows that he has in fact received it). But in normal contexts everyone would always understand seeing a letter as equivalent to reading it, unless the speaker went out of his way to clarify the fact that he hadn't actually done the second thing (for example, Sorry, I haven't actually read your letter [yet] - I['ve] only just found it.
1 Revisiting this answer, I realise that arguably I was "suckered" into assuming what might actually be a somewhat contrived context. Per my comment below (which might get deleted at some point), the fact that the apology was "spliced" into the standard "initial greeting" rhetorical question Hi, how are you? made me suppose the speaker was responding to the other person having already referenced the letter in his introductory utterance - maybe something like Hi, this is Mr Smith. I'm calling to see if you've got any recommendations for the problem I wrote you about.
In that context, it seems at least reasonable to me (but arguably not necessary) to use Past Perfect to reflect the fact that failing to have actually read it was a "sin of omission" effectively committed earlier than the (very recent) finding of the letter.
But that's just my take.