The "metal mesh backing" part makes me think you don't have real brick, but rather thin, brick-looking faux brick that are glued on. Whichever it is, it shouldn't present too much of a problem for removal and then replacement with either wall board or your tile work.
Unless you have overly-aggressive trades people where you live, I can't imagine "being taken advantage of" when getting estimates. It usually works like this: they look, they measure, they write down their number, they hand it to you, and then they leave. If they want $$$ for giving an estimate, send them on their way.