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If this doesn't remove the build-up, try a light abrasive cleaner like Gumption Paste. Use the same non-scratch scourer to gently work it in a circular motion before cleaning it off with clean water.
If neither of these options works, it could be that the tiles have been painted in the past and the paint has faded in some areas. If this is the case, you might need to consider painting the tiles with a suitable paint such as this Dulux Renovation Range Tiles & Benchtops Gloss White. - JacobZ
Definitely give the Gumption a go as JacobZ recommends. It's been a go-to product in our family for as long as I can remember. Yes its mildly abrasive, however you're going to need this or something possibly more abrasive if that doesn't work. It wont be a waste of money as you find plenty of other uses. Used gently with a microfibres cloth, I have removed pencil marks of walls from tiny little artists.
There is another product that has a bit more abrasion to it called the Pink Stuff. I've not used it myself but heard it's very good.
I also recommend the Scrub Daddy. It holds it condition extremely well. It's also another go to from burnt sauces in pots to scrubbing dirty work hands clean. Can be used with without cleaners. Not cheap but last for months as they can be dishwasher cleaned.
As a last resort, wire wool with Gumption may be an option? - Nailbag
