That version of "eagle button" has turned up many times previously here in the What-Is-It? forum. It is what button-collectors call a civilian Fashion button, made to loosely resemble an actual US Army 1902-to-presentday uniform button. That is why some components of the actual Great Seal Of The United States are missing. It's also why the eagle's head is very crudely depicted, with unusually skinny wings, the raised border is absent, and (here's a major ID-clue) the ribbon above the eagle's head looks like battletank's tread.
Compare your Fashion button's crude imagery with the finely detailed work on the actual US Army Great Seal buttons in the photo below.