Actually none of those moves by the Eagle were showing signs of attack. Large birds prefer the highest point to stand. The eagle was trying to move from his arm to his shoulder. They use their beaks to try and steady themselves as they transition. Sometimes pinches or bites can happen due to trying to hold on.
When the eagle was on the desk, he was only nervously warning Trump. Probably would have only bit him if he had actually gotten too close or touched the eagle.
I thought it was more funny that he messed his hair up. ;)