Is there a screen where the Oil Pressure Sending Unit is that needs to be cleaned when you replace it?

No, there isn't typically a separate screen on the oil pressure sending unit itself that needs cleaning during replacement. The filter for the engine's oil system is a separate, much larger component. Any debris that might clog the sending unit's port is usually removed during the sending unit's removal and replacement. However, if you find significant debris during the replacement process, it points to a larger issue that needs addressing, likely related to the overall engine oil system's cleanliness.