HutSiteDigger has it exactly right... a 1-piece brass "flatbutton" with an indented-lettering backmark, dug in the US, means 1810s-through-1830s.
Additional info:
Your button was manufactured for use on civilian clothing, though a few did get used on Militia uniforms. The backmark saying Extra Strong Gilt is one of the typical "quality-ratings" found on British-made brass buttons of that time period. Millions of them were imported into the US in that time period because the American button-making industry was not yet able to mass-produce them to meet the huge demand from the clothing industry. The War-of-1812, which was followed by a decade of patriotic American dislike of buying British-made products, means your button most probably arrived in the US sometime in the 1820s or early-1830s.