Wow. There is some kind of acid cleaner that can be used to clean grout haze, But try some vinegar. wipe it on, let it sit a few minutes and scrub gently...scotch brite pads work well but GENTLY or your glass will scratch if you apply elbow grease. also use a lot of water on the pads. try this a couple times.

as to the matte finish-you might like it better after cleaning, but the only thing that comes to mind is epoxy resin. it can be painted on thin thin coats. It can yellow with age, exposure to sunlight, and I dont know what else. and once you do it, you are stuck with it. Any other kind of sealer etc I can think of would be prone to peeling off with cleaning etc and that would look 10 times worse. and is it glass? or is the surface ceramic tile? that changes the game.

Interestingly enough, we rubbed a tiny bit of olive oil on a test tile and that GREATLY improved the finish and cleared the grout haze. Nothing to lose at this point - will add a slight sheen, won't retain water marks etc. Will use a mineral oil, odorless and colorless and will be careful not to get on grout. PS they are glass but do not have a smooth clear surface like typical glass tile.

Keep in mind that will attract dirt and dust in a kitchen. you will have to clean and reapply periodically. The vinegar will remove the grout haze and wont hurt the glass if you do that first. with the grout haze off, you might be happier.

Thanks, wackyweeder, I tried vinegar first and when that didn't work, the grout haze remover recommended by the manufacturer. The light coat of oil, although i realize that may have its own challenges, was the only thing that helped at all.