You cannot fix this. Generally, when the customer puts the checks in the wrong envelopes, one creditor is overpaid and another creditor is underpaid and any "damages" to the customer are in connection with the latter.
Assuming that you actually saw the checks when they were presented, you only had two choices, pay them or return them.
Legal machinations aside, that would be the core of my response. Something along the lines of, "This is your fault, not ours. Had we caught it as you imagine we should have and returned both checks neither bill would have been paid on time and you would have had late charges on both. Instead, we paid both items and now you only have problems with one creditor." (Obviously, you may want to smooth the sharp edges on that message, but it's still the right message.)
_________________________
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.