Would it be viable to install a screen in front of jet intakes to prevent them from sucking in birds?
Modern high-bypass turbofan engines work by pulling in immense volumes of air and accelerating it.  A screen as proposed would make that task far more difficult, which would ruin the efficiency of the engine.  It's also pretty well unnecessary.

Jets worldwide take plenty of birdstrikes every day.  Unless the pilots see it (hitting the windscreen will do that) or hear it (hitting something near the cockpit) or the bird goes into the engine core (which causes the smell of burned bird in the air conditioning), the chance that the crew knows about it before the next walk-around inspection is pretty slight.  The vast majority of birdstrikes are utterly inconsequential.  (Except for the bird -- ruins his day pretty thoroughly!)

Yes, there are a small number of very highly visible events where birds do disable an aircraft -- the "miracle on the Hudson" and the loss of an AWACS in Alaska come to mind, and there are others.  And it's possible for a birdstrike on an engine to cause significant damage IF the bird is large enough AND it goes into the core, but in the big picture, that is actually pretty uncommon.

Thus, the aircraft manufacturers and operators end up accepting the risk of a catastrophic birdstrike, because the alternative of protecting the engine as suggested is too expensive when the effects on the efficiency of the engine are considered.

One other point, bird flesh is pretty easy for an engine to chop up and digest.  If a big bird hits a metal shield at high speed, there would be the risk that the shield could be damaged enough that some of the metal would break apart and go into the engine as well, and THAT would cause far more damage than just the bird.

Fun video of stuff being shot into an engine during testing