Here is Mount Vernon's reply:
Thank you for contacting us regarding the “Warranted General Washington Handmade” banner or wrapper. This is the first time we have seen anything quite like this, and we do not have anything similar in our collection. As others noted, the terminology used, “Warranted” and “Handmade” is typical of that found on cigar boxes, labels, wrappers, and signs. Based on the style of the design, it likely dates to c. 1860-1900. In terms of the material, as you noted, it is woven, but it is possible it was woven from a thin metal thread rather than a natural fiber. I would recommend that you take it to a local museum, auction house, or appraiser for their opinion.
So, the search continues...