The brick was never finished to be shown so the joints weren't struck. Even cleaned up it will retain a rather rustic look. If that's in line with what you want you could clean the surface mortar off with muriatic acid. Though with the finished floors in the adjacent room that could be a problem. I used it inside the basement of my first house to clean up a brick wall we installed for a wood stove, but there I had a concrete floor and the framing and drywall hadn't been started yet. It takes a fair amount of water to do the muriatic acid bath, since you need to hose it down. Perhaps you could cover the floor with plastic sheeting, and make a dam out at the edges to contain the water, then use a wet dry vac to suck up the water as you go. You'd want to tape it off securely so it doesn't leak. What is below?