Oh gosh, I'm not sure what to recommend, and I am definitely not a cleaning expert by any stretch. My initial first reaction was that I don't think that Anderson hardwood is that shiny. Most of it is dull/matte finish and some of it satin. It is possible that previous to these deep cleaners coming in that someone may have tried to add some shine w/ a cleaning product of some sort that has wax in it. Not sure if that happened or not...but I know a lot of customers do that and don't realize that they are damaging the floors.
Anyway, my next reaction is that I think it's very risky to have anyone clean w/ any sort of steam cleaner and that usually is a no no and voids any warranties.
Here is a link to Anderson's cleaning care instructions, and I hope this helps.
http://www.andersonfloors.com/Care/Maintenance.aspxAs you read this, it sounds like what this company did is not recommended and voids the warranty, and I have a hunch they caused some bigger issues and made things worse. (Of course I can't see this, so I'm only guessing).
I would first call Anderson to see what they recommend so that you can try it in the area these guys didn't touch (and/or try in an area that doesn't matter such as a closet or area that will be covered by furniture or something.
Separately, I might see if you can pursue something w/ the cleaning company. I think they realized that they messed up and that's why they stopped.
Tricky situation for sure.
Debbie Gartner, aka The Flooring Girl
http://TheFlooringGirl.com