Remarkably enough, the Navy person who was sucked into the engine, survived.
Modern jet engines are built specifically to minimise damage from a bird strike.
The Hudson River incident was multiple Canada geese. Even if the engines had been restartable, there was no time to go through the restart procedures. The pilot made the "best choice" decision, and felt he would cause less fatalities either in the aircraft, or on the ground, by pancaking into the river. He very soon realised he would never make a landing field, and trying anything else other than the river would certainly have been worse.
He did a remarkably fine, cool- headed approach and execution. He followed all the rules.
A similar attempt to land into a rough ocean would most probably have been much more serious.
Filters are NOT practical, and would make no difference.
You have probably read or seen the story of the British Airways 747 that lost all 4 engines after flying into the pumice dust cloud from a volcano. They followed all the rules. After some considerable time and multiple tries to restart the engines, the crew managed to get all 4 running again, in time to gain height and reach the nearest airport. One engine did fail again when they flew back into the dust cloud, but they landed safely, even with poor visibility through the front due to the abrasiveness of the dust. They also had NO approach height help, they were flying by directional beacon, speed and altimeter only, right to touchdown!
What they DID have was good altitude when the failures occurred.
The aircraft was stripped of most of its paint as well.