Final answer:
The overlooked clue regarding how she killed John was the quilting method. The dialogue suggests Mrs. Wright strangled her husband, just as she intended to 'knot' the quilt.
Step-by-step explanation:
The clue that men overlooked which gives information about how she killed John is the quilting. In the critical exchange, two women discuss whether the unfinished quilt was going to be quilted or knotted (another method of finishing a quilt), and this eventually ties back to the method of the murder: John Wright was killed by being strangled with a rope, which relates metaphorically to the act of 'knotting.' The women's realization that Mrs. Wright would 'knot' the quilt mirrors the way that John was killed, and this becomes the symbolic representation of how she strangled her husband, effectively knitting the pieces of the crime together.