Not sure it has much to do with who owns the property
but rather who has control of the Eagle.
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Bald Eagle Protection Act of 1940. This act was expanded to include the golden
eagle in 1962.[1] Since the original Act, the Bald and Golden Eagle Protection Act
has been amended several times. It currently prohibits anyone, without a permit
issued by the Secretary of the Interior, from “taking” bald eagles. Taking is
described to include their parts, nests, or eggs, molesting or disturbing the birds.
The Act provides criminal penalties for persons who “take, possess, sell,
purchase, barter, offer to sell, purchase or barter, transport, export or import, at
any time or any manner, any bald eagle ... [or any golden eagle], alive or dead, or any
part, nest, or egg thereof.”[2]
https://en.wikipedia.org/wiki/Bald_and_Golden_Eagle_Protection_Act
While I agree in principle that it might be a good idea for the feds to have limited power to define and protect endangered species, while the states automatically have these powers under the 10th Amendment for non-constitutionally owned federal land, it remains that the states have never expressly constitutionally delegated to the feds the specific power to address INTRAstate wildlife issues.
"From the accepted doctrine that the United States is a government of delegated powers, it follows that those not expressly granted, or reasonably to be implied from such as are conferred, are reserved to the states, or to the people. To forestall any suggestion to the contrary, the Tenth Amendment was adopted. The same proposition, otherwise stated, is that powers not granted are prohibited [emphasis added].” —United States v. Butler, 1936.
Consider that corrupt, post-17th Amendment ratification federal lawmakers will promise citizens and illegal aliens everything under sun in order to win their votes, regardless if the feds actually have no express constitutional authority to deal with an issue.