To me, it looks like the glaze is partially worn off, so trying to get an even look across the whole thing won't really be possible. If he doesn't like that 'character', it may call for replacing the tile. It's almost certainly on a mud bed which will be some hard work to get out. The mud beneath is likely at least 1.5" thick, and anything new would likely need to address not only the tear out, but dealing with the subflooring. There are people around that can replicate that install method, but lots more that only know how to do it with more modern materials. There's nothing wrong with a mud bed...it's often an ideal way to install it, as if those floors are original, at nearly 100-years should attest to.
There are a bunch of grout cleaners out there, but it looks like a grey grout, and may not actually improve much with any cleaning.
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Jim DeBruycker
Not a pro, multiple Schluter Workshops (Schluterville and 2013 and 2014 at Schluter Headquarters), Mapei Training 2014, Laticrete Workshop 2014, Custom Building Products Workshop 2015, and Longtime Forum Participant.
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