Treated water is using something like Prime water conditioner which removes Chlorine, Chloramines, and heavy metals. (Prime and a few others will also detoxify the Ammonia, Nitrites and Nitrates.)
So at the base level , a "dechlorinator". Not all of the treatments will take care of all of Ammonia, Nitrites and Nitrates. So ANY time you use water, even for cleaning fish stuff from the tank I would use a Treatment like Prime, just because of the possibility of heavy metals in your well water, since as you said it doesn't have Chlorine, so you wouldn't be worried about that. If you use a UV sterilizer to make your water safe to drink, then it still wouldn't take out or neutralize any heavy metals.
You can read up on Prime and how it works. I am not the scientific explainer. lol
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Congrats to you for wanting to take excellent care of your fish. Just know that even with all that you can physically do for them sometimes things happen and they get ill or die, so, in advance, don't be hard on yourself if it does happen.
You are obviously not one who could care less how many fish die, as long as you just have something pretty to look at. Yay!!!
First I will say, I am just a human being trying to help and you will always need to research, and learn and make any final decisions on any care or actions for your critters and that goes on anything here.
You, I can tell, are very concerned about the filter pads. Yes they are expensive, and very valuable when they are teaming with BB.
So just think of it as a beneficial bacteria farm in a filter pad. Your objective is to create a bustling invisible to the naked eye, BB farm and keep it growing and happy. Cleaning it will make you happy, but not make the BB happy. Chlorine will kill it as might heavy metals and stuff (in case any one else reading this has city water)
So a vigorous swishing in your removed water from a pwc (or fresh treated water) will actually loose some of the bb but there should be plenty left after the colony gets established, therefore enabling a happy nitrogen cycle in your tank, and a happy fish tank and stable water parameters.
So keep the BB farm growing!!!
Now if you must remove a BB farm filter pad it will be damaging for the tank water parameters.
Seriously, I think you can slide 2 filter pads in there. If not a filter pad, maybe a rectangle of bulk filter and you could replace THAT more frequently. Considering it takes 4-6 weeks to establish a good BB farm colony, you can see the very serious downside to throwing out a pad every month. (and throwing out the little BB guys who work so hard to keep your tank in "perfect" order.)
Hope you can feel happy about growing a BB farm now...