The word "that" has several meanings in Poland. The translation of that word depends on the case. "The translation of THAT word depends on the case." In this case the translation of "that" is "tego", but nevermind that. When we are talking about that old woman, we can use forms "ta" or "tamta", both are correct and they depend on the distance you are from that old woman. If she is very close you'd use "ta", if she's a bit farther you'd use "tamta". Nevertheless, both forms should be correct here.