My most recent job was a 1000 square foot area of brand new 18" by 18" tiles. The grade of the travertine, I would rate a C. Yes you can get various grades of travertine. The better the grade the less grout filler you will see in the tile and it will look more like marble. As the old saying goes, you get what you pay for. I always recommend getting the best grade you can find, as it will have the least amount of grout in it and it will polish uniformly. Secondly, that grout they put in at the factory looks good at first but falls out over time. When that happens, it is wisest to fill the missing grout with epoxy as it is much stronger and blends better with a polished floor. You can't make grout shiny. It is sand and that is why you should avoid cheap Travertine. Better yet, by marble. It is more durable and cheaper to maintain in the long run.
So on to the floor. Afterglow (me) has steam cleaning high-pressure cleaning capabilities run by a highly modified truck-mounted unit. Most restoration (nearly all of them actually) don't have these machines.They use portable carpet machines which are glorified shop vacuums. No heat, no pressure, and not much vacuum. No comparison.
So they want to diamond grind everything to get it clean and charge you more even though it is an oversold process. Secondly with Travertine, if you grind in the more coarse grits you get into the grout layers and then you will have problems when you move up on the grinding scale to more finish cutters/ polishing, as now you are trying to polish sand.
So what do most companies do? They tell you they are going to diamond grind your floor but in actuality they start at higher grits and fly over the floor. A lot of fluff. But technically diamond grinding. Then they still have to paste polish the floor after and seal. All the while all that dust from the installer is still in the pores of the tile plus whatever they added while diamond grinding with a 400 and 800 cut. Real diamond grinding to flatten a floor goes all the way down to 50 grit. They won't go that low for what they quote. If the tile layer left lippage ( when two adjoining tiles are not flat against each other), you will need to at least start at a 100 grit, then 220 , then 400, then 800, and possibly 1800 after that. Then you slowly paste polish the floor, which is like a 2000 grit finish. The final touch, liberally seal the floor with a penetrating sealer.
If you diamond grind at 400 as a starting point, at best you will just round over the lippage or bevel it. Tile layers are notorious for doing this and are lousy at it and also skip steps.
If you have to flatten the floor you have to charge for it and it won't be a one day process. You will have to go slow and go through all the grits to get a high shine. A very slow paste polish is necessary also.
One other note. I steam clean the floor at 220 degrees at 2500 p.s.i. to clean out the pores and if any grout is going to break loose it will right then and there. I will then fill it with epoxy. Otherwise, you can wait a year or two and it will fall out on it's own. Wouldn't you rather have it fall out on me? I will fix it before I paste polish.
So next time you get a real cheap quote to get your travertine polished, cleaned and sealed, remember you get what you pay for. I am an owner operator and usually will only do 1 house a week. and the last thing I want to do is go back and correct things not done right the first time.