Its not American Navy. I suspect its a civilian blazer button but the foul anchor design has been used by the British Navy and Merchant Marines.
We have discussed these fouled anchor buttons here before but the others didnt have a backmark.
In 1774 a foul anchor surrounded by rope edging took the place of the rose and in 1787 the same device with the addition of a wreath of laurel leaves was adopted for Admirals. When the Merchant Navy started to use the foul anchor device, a crown was added for all naval officers in 1812. The same basic design remains in use today.
The foul anchor device itself was first recorded in use in the seal of the Lord High Admiral of Scotland in 1402. It was subsequently adopted in the Admiralty seal and by a large number of navies throughout the world. The rope 'fouling' has no specific twist and may be deemed to be correct however it fits around the anchorhttp://www.colchestertreasurehunting.co.uk/navy buttons.htm