Water marks on matt Regal tiles

[MLouB72]

We had matt slate Regal tiles laid in our kitchen three years ago and they are starting to look really water damaged. We do use a non-abrasive floor cleaner but I think we might have damaged them somehow. Is there anything we can do/use to restore them? Any suggestions gratefully received!

 

[Tile Marble Granite]

Stop using chemicals to clean up the floor. Is that real slate? Hard to tell by picture

 

[MLouB72]

Stop using chemicals to clean up the floor. Is that real slate? Hard to tell by picture

No, it's matt porcelain. And yes, obviously using chemicals isn't a good idea, but what I'm after is suggestions to get rid of the marks.