Which button is re-cut and how can you tell?
Hopefully this will illustrate the variety.
The first image is a close up of my recut button. The second image is a different stamp without the recut.
What you often see is the recut areas stand out, especially on a stamp printed with a worn plate. That's what my stamp shows.
Now look at the button lines on the second image. See that they pretty well match the lines of the collar and bust area.