Indepedendently, I think if either Bandit or Syr’Nj had acted less emotionally during the first confrontation, an explanation from Bandit might have helped matters. But after that scene, I don’t think it could have done much good. Syr’Nj had cemented her mental image of Bandit as an unreliable loose outlaw, and Bandit hers of Syr’Nj as the boss who’ll never listen. You can’t reason against her, because reason is her weapon of choice, and she will out-reason you if you try.
At that point, any attempt to explain would have come across as trying to re-frame your own past failures, independent of which of the two was making that attempt. I think the only thing that might help is if Byron came to a different conviction about what happened and annoyed Syr’Nj with it until she gave in (nobody else has a chance to get Syr’Nj to listen for long enough). But even then, it’s hard to imagine Syr’Nj and Bandit ever becoming anything resembling friends. Way more likely (though still really unlikely) that Byron and Bandit teamed up sometime in the future.