I found 'that's a pity' on http://www.ldoceonline.com/dictionary/pity_1 Definition#1
Not a teacher.
Student or Learner
I was told recently that "That's a pity" is wrong, it should be "It's a pity" instead. Is it really so? Is "that" completely wrong in this phrase?
I think this might be a partial recollection of the fact you can't say 'That's a pity that we can't go'. Or, to put it generally, 'That's a pity' is fine if the sentence stops there. But if, in the same sentence, you go on to specify whatever's regrettable, you have to start 'It's a pity...'.