It seems that tea with lime water (hard water) tastes different.
Different enough that tea manufacturers have a different product to cope with the difference in taste.
My question is: Why does tea with hard water (lime) taste different?
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This seems to be answered directly on the Yorkshire Tea page.
Before we get cracking, here’s some background about Yorkshire Tea and hard water to bear in mind. When deciding which teas our buyers will select to put in the Yorkshire Tea blend, they taste every single one in both soft and hard water. This enables them to create not only Yorkshire Tea, but also Yorkshire Tea for Hard Water, a blend that’s perfectly suited to… you guessed it.
Seems to imply that there are different blends of tea that taste better in hard water and soft water that they are accommodating for.
To answer the question "Why does tea with hard water (lime) taste different?", it has to do with the higher concentrations of calcium and magnesium that your taste buds will pick up on. From the Yorkshire Tea page, it seems they make two different blends of tea with the blend for hard water stating:
The tap water in hard water areas contains lots of minerals, which can make tea taste darker and thicker. With a few clever tweaks, we’ve made a blend to balance that out – so you can enjoy a proper brew, wherever you live.