Thank you for the effort of making a well-focused closeup photo of what remains of your brass 2-piece button's backmark. It seems to have what is called "Serifed" lettering (see the diagram below) which was common in pre-1900s backmarks, afterward superceded by "plain block" lettering. Combining the following clues: 1- the presence of Serifed lettering, 2- the presence of an "Extra Quality" backmark (common in the 1800s, much less often seen in the 1900s), 3- the "construction" of your button's back (having a brazed-on loop), I believe your button dates anywhere from the mid-1830s to the end of the 1800s. It is more probably from the earlier part of that time-range than the later part.