The inlet screen is a separate "plastic/screen unit" that attaches to the inlet side of the water pump. If your pump is a Flojet pump with the blue locking clips to hole the inlet/outlet hoses, then it's a simple process to add the inlet screen. It's available on Amazon for about $10.
https://www.amazon.com/Flojet-017403...%2C183&sr=8-14
If your pump is a ShurFlo, then it's a different style, based on the fittings (probably pressure screw on fittings) for your pump.
With either type, the stainless steel screen in the inlet screen "filters out" anything large enough to damage or get caught in the rubber diaphragm/roller portion of the pump head. There's not a "backflow valve" in the normal sense, rather the diaphragm/rollers act as the backflow valve, so anything that causes a problem with the diaphragm "laying flat" will cause a leak through the pump and into the water tank...
As for "never having used your water pump, the dealership "should have" filled the water tank and tested the system for leaks during the PDI, so it's possible that when they "ran the pump during testing" they picked up some shavings... Then again, your problem may be from an "actual defect in the pump" not related to shavings from the tank...
If the dealership gave you a replacement and don't require you to return the bad pump, you can take it apart, check for foreign matter in the pump head, reassemble it and you'll have an "emergency replacement pump" for future problems..... I store my replacement next to the pump, so it's always ready as a "threat against failure"
Here are photos of the FloJet strainer with the blue clips (linked above) and a type that connects in the hose of the ShurFlo pump.