I actually work customer service for a bank. Most of the time you are able to get courtesy refunds every so often. Like 1 every 6 months or 12 months. Depends on how much business you are bringing through.
So, if this if your first late payment I'm quite confident you could get it refunded. I probably wouldn't try to tell a story. Just call, verify yourself, and say something to the term of "I recently slipped up and got my payment in a bit late. Considering my flawless history is it possible for you to waive that fee as a courtesy?". That way the rep (who has a goal talk time on the phone) doesn't have to hear an excuse and it sounds very professional. They can tell you yes, and get you off the phone quickly.
Lastly, don't be afraid to ask. Like it was mentioned previously, the worst that can happen is they say no.
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