What about anonymous apologies?
Years ago, while working as a bartender at Nina's, a local bar on Columbus Drive in Chicago, I once (innocently) gypped a customer out of $10. He gave me $20 to pay for his drink, but I gave him change for a ten. He said I still owed him change.
I didn't think he'd given me a twenty, so I checked the drawer to see if I'd put a 20 in the 10's slot. Nope.
I politely disagreed with the customer, and he just shrugged and let it go.
The next day when I showed up for work, the owner informed me that my drawer was over by $10. I was mortified!
I told him what had happened, and he told me what I should have done was taken his name and number/address.
That had never occurred to me (I guess because I was sure he'd given me what I thought he had).
I've always wished there were some way I could make that right. He was such a gentleman about it - he didn't get angry or belligerent. He and his companion just finished their drinks and left.
Nina's is long gone, and I'm sure it hasn't remained in his memory, but for some reason it's a "woulda-shoulda-coulda" that I just can't forget.
So, kind sir, whoever you are, I offer my sincerest apologies for my mistake and my inexperience, and hope that good fortune has smiled upon you and yours since then.