That's that ou that takes care of that é uma expressão com o sentido de '...e pronto', usada quando não se tem mais nada o que fazer/dizer.
Dad said he wouldn't buy you a new car, and that's that.

Dad said he wouldn't buy you a new car, and that's that.
(O pai disse que não vai comprar um carro novo para você e pronto.)
I called Tom and told him our relationship is over, and that takes care of that. "That's that."
I called Tom and told him our relationship is over, and that takes care of that. "That's that."
(Eu ligue para Tom e disse a ele que nossa relação está acabada e pronto.)