We've only recently had to deal with CITES issues, but the object in question was recently made ethnographic object with feathers (not eagle).
Most of what we deal with involves the UNESCO Convention for Cultural Property.
So I can draw a parallel - we look at how, when, where the object was acquired.
The coat is 1900-1950; CITES is circa 1973.
Alaska and Washington are both United States so no international borders are involved.
Pinnipeds are protected under US law (again post 1970s), but they might not be on CITES endangered list.
You would have to know which type of seal to see what its status was.
Objects containing eagle feathers are more problematic given the restrictions and the exemptions.
There are official repositories for eagle remains, but objects with feathers/bones aren't generally mentioned.
Hope this helps. Would love to hear more from others.
Chrisso Boulis
Registrar Records
Penn Museum
T: 215-898-4088