Hold it up to the light and try to see whether there is any evidence of fibers running criss cross in the paper itself. If you can see criss cross patterns, that would mean it printed on "LAyered paper" or laid paper in the trade. Laid paper is a sign of greater age and would have been used during the early Revolution period. If the poster is real, it could be worth many thousands of dollars. If its a repro, its worth whatever the run was priced at since repros of documents dont hold value at all.
I do picking of antiques and see repros of historical documenst all the time. However, every so often, someone finds a real one and the sky could be the limit. About 12 years ago, at a place in Adamstown Pa, a junk dealer sold a print to a picker who took the time to remove the print from the frame and mat. Behind the mat was a secondary copy of the Declaration of Independence , a number of which were printed in Philadelphia about July 5 to 8th 1776 for delivery to the colonial capitals for public display. Only a few of these copies remain and the picker who found the second printing of the Declaration of Independence sold it for 2 million dollars. The same document has sold several time since and latest price transaction was about 12 million dollars.
So, be careful before you trash it. The recruitment poster wont be worth 2 million but it could be worth from 10 to 20K$ ( provenance and condition are everything)
Go to a place like Winterthur Museum of American Art and Antiques rather than a private dealer. A dealer will be tempted to undervalue it and , if you get a good appraiser that has no personal attachment to its outcome, is way better.