'Schindler's List' question

Okay, so this has been bugging me for ten years…
I love this movie. I’ve seen it at least a dozen times. It’s hard to imagine a more perfectly crafted film. But there’s one thing I don’t get…

At the end of the film, the scene outside the factory when Schindler breaks down because he could have saved more people, we see Schindler huddled on the bumper of his car and everybody gathering around to hug him.

Then the camera turns away and follows a woman walking away from the car. She’s holding what appears to be a shirt and unbuttoning it. What’s up with that?

I think the shirt is a striped one from the concentration camp, it’s hard to be sure. But, in any case, what’s the point of that scene? Is there some artistic or religious significance that I’ve been too dense to notice?

Didn’t they dress Schindler as a prisoner in order to keep him from being taken prisoner by the Reds?

Yes they were giving the Schindlers prisoner clothes to disguise them.