Hard plastic stuff on the screen is the nylon from the upper sprocket on the timing chain. If the timing chain has never been replaced, it needs it now. If it was replaced, they were sloppy doing the job and didn't drop and clean the pan. Worth checking while you are this far into the engine.
Melling has a line of pumps (standard, high volume, high pressure) in there performance line that come with a new upgraded oil pump driveshaft. Not the fancy smooth ARP version. Looks like stock. But better materials/heat treated. Worth a look as you get a better pump than the standard pump and better shaft for less than buying them separate. The oil pump adds a lower support that you don't normally get. The pressure relief is also adjustable (at least on some).
I replaced the timing chain myself when I did my explorer serpentine conversion. Don't remember seeing nylon on the upper sprocket of my particular timing chain when I installed it. Looking up at the timing chain from the bottom with the oil pump removed, everything looked good.. I went with a standard Melling pump, but upgraded the shaft to ARP. Just waiting for the sealant to cure before I try it out. I think I'm pretty lucky to have caught it before driving it. It was hard to start, then I heard something fall (was the oil shaft falling into the oil pan)