Most likely the button manufacturer struck too many planchettes with the eagle/anchor die and didn't want to waste them so they were repurposed as civilian buttons. Perhaps they were anticipating an order from the US Navy that never came to fruition. It's interesting that the back mark isn't present on the front. I always assumed the buttons were struck between two dies just like coins which would impress an obverse and reverse simultaneously. This button would suggest that they didn't impress the back mark until the button had been destined for a particular finishing process (i.e. double gilt, treble gilt, silver wash).
By the way, that button is remarkably well preserved. That's a fantastic specimen you have there!