Dear {Name},
I am so sorry for telling that joke. I shouldn't even call it a joke. It wasn't funny, and you were right to be {angry/hurt}.
I really have no excuse, though upon reflecting on my behavior I now realize I was just trying to get attention. Ugh; what a jerk. I still can't believe I thought that "joke" was in any way appropriate.
Please know that this has been a learning experience for me. I deserve any backlash or negative thoughts coming my way. If you can find a way to get past this, your forgiveness would be more than I deserve.
Sincerely,
{Name}
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