Thanks for your suggestions. Having failed to remove it with a toothbrush, I tried carefully scratching a patch of the deposit with a pin. It didn't even scratch the surface!
I've attached a couple of photos so you can see the deposit and that it looks like something stuck to the surface, rather than a reaction in the glass itself. Perhaps your suggestion that someone has mixed something in the lid is right.
Whatever it is, I'll leave it there rather than risk damaging the glass with any more of my amateur attempts at removal.