To the above question you could add the following subsequent questions. How does her mind explain such an act of kindness? Does she remember that for the rest of her life?
These three questions were asked on Quora.com. I wish to try and answer the questions. The first question can be answered by saying that the cat will feel content or more content than she was when struggling to survive as a stray (by which I mean a lost domestic cat).
Initial stress

Initially, the act of being rescued is not very pleasant for a stray cat because she is normally dealing with strange people. This is particularly the case if rescued from a disaster of some sort such as a house fire or storm flooding.
She will accept the process of being rescued but end up in a rescue center which is also stressful. So her first experiences of rescue are not good ones. Hopefully, she is then adopted into a nice home where she will be fed good food, be warm and be treated nicely. If the ambient mood is excellent then all the elements of a contented cat are in place. Accordingly, she will feel content.
Increased contentment
Therefore, the end result of being rescued is that a stray cat will feel more content and relaxed. She will also recognize in her feline way the friendship offered by her new human companion(s). I believe that domestic cats essentially relate to human caretakers as adult cats. In fact, they relate to their owners as surrogate mothers most of the time.
This puts the domestic cat in the role of a kitten. But she’s well looked after, reassured and feels safe. This must elicit a response of contentment. We know that domestic cats form friendships with other cats and of course with their human caretakers. Therefore she has a friend as well. Domestic cats are quite sociable and friendships also make them more content. Overall, a stray cat feels much better once she has been rescued.
Recognize kindness?
As to how her mind explains such an act of kindness; this is more difficult to answer. It requires a sophisticated mind to realize and gauge an ‘act of kindness’ offered towards one. I’m not completely sure that domestic cats recognize an act of kindness but they do recognize an act which makes them feel better. They also recognize the act is from a friend or a friendly animal. And therefore rather than assessing the act as one of ‘kindness’ (a human concept) she will regard the act as one of friendship.
Remembering the rescue?
The third question is about memory. In my view, domestic cats have good long-term memories. They remember bad events and avoid the circumstances under which the events took place. Domestic cats can be trained which also reinforces the view that they have good memories. Accordingly a stray cat will remember the specific act of being rescued as one which changed her life resulting in a much better life thereafter. She will remember that she made a friend on the day that she was rescued in the form of a very large, rather strange looking cat who became her surrogate mother.
References
That, in my view is how I see it. They are personal views. I have not referred to any books or reference manuals in answering these questions. I have answered them just based upon personal experience and my feeling towards how stray and domestic cats think.
P.S.
Rescuing cats is great for the welfare of the person doing the rescuing! It can be therapy for some.
Note: I selected stray cats as the recipients of rescue because the answer would be very different for feral cats. True feral cats don’t need rescuing. They need to be left alone but cared for.
Note: sources for news articles are carefully selected but the news is often not independently verified.