I have had very good luck with flushing them out. Start with leaving the hot water on,cold water off at the faucets. Remove the cold water hose at the valve. Set the washer to a warm fill and put a towel under the valve,start the washer and while it is filling stick your small finger inside the cold inlet on the valve and gently scratch the screen. reverse and do the same for the hot water. Been doing this way for 25+ years and never had a problem with sediment bypassing and sticking the valve open. Removing the screens you have a possibility of sediment causing a water valve failure sticking open and flooding.