Welcome, Carl,
The gritty substance is likely grout, and it could well be that someone previously added some type of caulk over those joints in an attempt to seal the joints.
To re-grout those joints you'll need to remove the old caulk and dig out the old grout to a depth equal to about 2/3rd's the thickness of the tile. Keep pin mind, though, that the tile to tub joint should be caulked, not grouted, to allow for differential movement between the tile and tub. A 100% silicone caulk is what you want in that joint.
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Dan
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If I recall correctly my memory is excellent, but my ability to access it is intermittent.
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