Look deeper into the meaning of 생기다: to be formed, to appear, to happen.
The ugliness is a trait that emerged/happened in the past. Consider the expression: her face is disfigured. Disfigured is in the past tense. Although the trait of the disfigurement is ongoing, the statement is about a past event that caused it.
The Anglophone mentality is that the person is “uglying” (present continuous). The Korean mentality is that the person became ugly at a past point in time and that ugliness carries into the present where a person making an observation will simply say “hey that person became ugly at some point in the past!”
I wrote more here: https://www.duolingo.com/comment/24492618
the verb "to be ugly" in korean translates better to "was poorly formed" as in the ugliness was present when you were formed, which is something that would make me cry if someone told me this in real life.
its just something koreans conjugate past tense without realizing it or paying it much attention.
I don't know in what context you are using this in, but i will assume you are talking about a woman being ugly.
그 여자가. The fact that the woman is being talked about makes her the 'who' of the sentence. The subject being the woman, for example if in conversation with someone and the person asked who is ugly then this would be right.
그 여자는 would be used to emphasise the 'what' of the sentence. Like if someone asked what woman is ugly then you would say 그 여자는 is ugly.
This Talk To Me In Korean video really helped. https://www.youtube.com/watch?v=fCxLNRLntc0
If I am wrong please correct me, I would hate to give anyone the wrong answer.