She wasn't exactly sure why it had a strap running straight along the back. I hadn't seen anything like it myself. The big questions were how was it supposed to be held and what was the strap for?
After some looking around in my reference books I came across an example in a 1908 Sears Roebuck catalogue and an illustration on how to wear it (see bottom photo). It's apparently called a vanity purse and you slip your hand straight down with the palm of your hand facing the side of your body. Since I did not come across any photos like this on the Internet or references to "vanity purses" as Sears had referred to this style I thought I would share the reference (excuse the quality).
The vanity purse seems a bit awkward to carry which might be why we don't see this style anymore. Today we see the more common clutch purse for evening wear which you simply wrap your hand around and hold.
(1908 Sears, Roebuck Catalogue: A Treasured Replica from the Archives of History, Ed. Joseph J. Schroeder, Jr., published by Digest Books Inc. Northfield Illinois, 1969. Vanity purses listed on page 1000.)