AWS checking for re-hirebility with previous employer

I was terminated by one of the companies I have worked for (currently employed by a different company), and probably tagged as "NO" for re-hirebility. I have accepted the offer from AWS Singapore - would the background reference check ask previous employers about re-hirebility/reason for leaving? Can any HR from AWS Singapore verify this? Also would it help if I produce a letter to prove that I worked in that company that terminated me in the past, so that they won't contact them? (The company is was a huge bank BTW) Thanks a bunch!