Spats is correct... your brass tent-rope adjuster/tightener's design was invented and patented in 1880 by Mr. H. B. Thompson. See the original US Patent diagram showing it, below. As the diagram shows, it was called a "tent slip." It was first issued for US Army use in 1889 -- 24 years after the end of the civil war. See the scan of the 1889 Army Order about it, below.
But of course, you'll see them for sale on Ebay as a being a civil war relic. Friendly advice: NEVER trust an Ebay seller when the words "civil war" are in the item's description. Instead, check to make sure. Grab the Ebay photo of the item and post it here.
The reason these 1880s-&-later tent-rope adjusters turn up in civil war camp sites is:
Until the late-20th-Century, a good site for an encampment tends to stay a good campsite, and therefore got used repeatedly whenever the Army does troop-training in that area. I personally dug one of these in a Confederate campsite near Fort Fisher NC.
About time-dating your Thompson tent-slip:
Ones made during the first 17 years after the Patent was issued were marked with the patent's date. After the patent expired, they were unmarked. Therefore, since yours appears to be unmarked, it was made sometime after 1897.
