+ 1 on cleaning out the screen. It's pretty easy with a siphon or maybe even a turkey baster. This is what I got:
Amazon.com: Slippery Pete Fluid Pump for QUART BOTTLES - Transfer Gear Oil, Transmission and Differential Fluid With This 5cc Hand Pump (NOT FOR Red Line Quarts!) (1) : Automotive
When I replaced my PS hoses, I pumped out the fluid in the reservoir and I saw black chunky flakes getting siphoned. My guess is that's what you have as well. Tbh, it shouldn't take long to do. Just pump out as much as you can, maybe even refill the reservoir a few times to repeat the cycle.
