Solder debris in multi zone hot water baseboard boiler heating system blocking valves
Whether a screen will fix your problem or not depends on several things.


Particle size. Only if the screen is fine enough it will retend the particles.
Amount of dirt. If the debris in your circulation is more than the few particles it might sooner or later just clog the screen. Perhaps the screen needs more regular service than every other device.
Origin and distribution of the particles. You mention that the problems rose also after service. Then particles might migrate against normal flow direction during service periods when the pumps are shut down for longer time. A single screen before the pumps and their respective check valves then won't protect you. Where the affected check valves before or after the pumps (from flow direction)? If after this could indicate debris coming down against normal flow direction during times with no water flow. 


The HVAC-company servicing my parent's home added kind of siphons in the system. It was to catch spurious air bubbles but also catches debris. They consist of short vertical tubings with at least twice the normal piping diameter. On top of the tubes they mounted an automatic bleeding valve. The water entered the big tube from the side and left it at the other side. Air was catched on the top and debris on the bottom due to the reduced flow speed inside this vessel. I don't know if this works in your case, but you might talk about this with your HVAC company.