if the pellet stayed with the starling and the eagle eat the pellet and it is lead that is problem for the eagle, lead poisoning
would one pellet do that, unknown to me but in Washington state we have geese still getting poisoned by old lead shot
If an asteroid of approximately six statute miles in diameter, traveling at approximately 64,000 miles per hour, landed within a 300 mile radius of the tree the eagle is standing on, and subsequently the eagle was struck by lightening, caused by the static buildup on the asteroid's surface as it traveled through the Earth's atmosphere, then the eagle wouldn't give a poop about the lead in the bird...this being due to the presence of numerous and more important personal difficulties at that specific time. Eagles are clever like that!
Kindly 'Ol Uncle