Yes it just unscrews. Water pump switch off. I usually turn the water pump switch off and open a tap for just a few seconds to take the serious pressure off the system before I mess with it.
For winterizing, if just blowing out the lines with air the strainer is normally removed, emptied of water, and either left off for the winter(which is what I do) or put back on empty after the pump has been run dry.
If antifreeze is used the strainer may never have been touched. But, it could still be a touch loose.
Try removing it, clean out an debris and then screw it back on and turn on the pump to see if it holds pressure. Make sure the threads are clean as well. No grains of sand or anything like that.
2008 2500hd Silverado Duramax
2011 Northern Lite 8.5 lite
2006 Wildcat 27bhwb fifth wheel
2009 Lance 830 (sold)