I have been unable to find any definite story of a parabolic woman who collected valueless things. However a closer reading of the G. K. Chesterton story, especially reading the context of the quotes above, reveal that when the two specific items are mentioned, an old doctor's brass-plate and a wooden leg, they refer to a (male) character in the story who laid a ruse using a discarded doctor's name plate and an artificial leg.
The question thus becomes, If the allegorical woman has been used as an archetype ofa metaphor for a particular individual, male or female, to the extent that she is said to have bought one or more apparently useless (but very specific) items that the same individual had bought, is the story of the woman actually a proverb that has been modified to suit the current situation?
From this context it may be inferred that the question "Do you know the story of the woman who collected ----" with one or more apparently useless items in the blank, is an unusual/old idiom intended to convey that the apparently valueless item in question can, in the right circumstances, be very useful.
The origin of the idiom (if indeed it is one) has not been found.