My guess is that if you have a filter screen in your outside water inlet, you remove it, turn it around and insert it backwards so that the protruding side of the screen pushes against the check valve to open it. The only advantage I see in this is that only one person in required to do the final step of pumping the RV antifreeze into that part of the water line. Otherwise, you need two people: one outside to hold the check valve open while the other inside operates the pump. If this was the case, the same result could have been accomplished by simply opening any faucet rather than subjecting the check valve's filter screen to possible damage by using it in an unconventional manner.
You must have a valve open somewhere so there is no pressure in the water line when you prime the pump with antifreeze, otherwise, when you start the pump, it will pressurize the water line and reduce the amount of suction necessary to draw the antifreeze into the pump.
When I winterize (and I just did yesterday), I always begin pumping the antifreeze to the faucet that's the highest and/or furthest from the pump and work my way back. So, for my RV, the order is kitchen sink, bathroom sink, bathtub and toilet. Your sequence may be different, and with fewer/more faucets.
Running the antifreeze to the water inlet is always done last. You must, momentarily, open/close a faucet to depressurize the water line before performing this or you won't be able press in the release to open the water inlet check valve.
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TV: 2009 GMC Sierra 2500HD | Crew Cab | Std. Box | 4WD | Duramax/Allison
RV: 2000 Jayco Eagle 266 | FBS | TT -- 1986 Coleman Laramie pop-up -- Still in the family!!!