I keep seeing 1877-1948. I also see slightly different variations of this backmark on "Indian War Era" buttons. I am just trying get a tighter date than 71 years.
By starting with the back mark book, he states Allien left Horstmann and started on his own in 1877. He futhers shows that back mark used on SU 8 & 9 in Alberts book. In looking at SU8, it states the button was adapted in 1898. SU9 shows the button was revised in 1923. So your face of the button should show you which date is closer.
Turtlefoot, yours is definitely the one from 1923. The most obvious change is the head of the eagle. It was looking right as we see it, and, as in yours, it is looking left as we see it.