What if Deadlock cut/blew off McCrees arm at some point because he had the tattoo and they viewed him as a traitor so they said 'fuck you'

That’s definitely plausible. Someone else brought to our attention that since they’re technically some kind of biker gang, they’d cut it off because he’s no longer part of their crew. When you leave a biker gang, they want your patches (i.e. the vest you wear while you’re in the gang that shows if you’re a ‘prospect’ or full-fledged member) and they’ll even force you to remove the tattoos you’ve gotten that’re related to the gang.

So it’s possible they ran into McCree after Overwatch disbanded, saw that he was all on his own, and cornered him so they could cut off the arm.