We often use the reflexive form of speech as a means of emphasizing something. And in all such cases our reflexive expressions can be “straightened out”. Thus we use the expression, “If I can't, I can't”, “I am as I am”, “It is just what it is”, also “That's that.” This latter phrase means as much as, “That's settled”, but why should we express “That's settled” by “That's that”? The answer can be given by laying before ourselves a series of interpretations which make a transition between the two expressions.

So
Thus

for “That's settled” I will say, “The matter is closed.” And this expression, as it were, files the matter and shelves it. And filing it is like drawing a line around it, as one sometimes draws a line around the result of a calculation, thereby marking it as final. But this also makes it stand out, it is a way of emphasizing it. And what the expression, “That's that” does is to emphasize the “That”.

(2015–) Wittgenstein Source Bergen Nachlass Edition (WS-BNE). Edited by the Wittgenstein Archives at the University of Bergen under the direction of Alois Pichler. In: Wittgenstein Source, curated by Alois Pichler (2009–) and Joseph Wang-Kathrein (2020–). (N) Bergen: WAB.