If I may:
Those filter elements can offer up to 300gal of usable water...but that is under the VERY best of conditions. 200 gallons is not going to happen with a conventional water filter if you are pumping from even remotely contaminated water. This also requires that you clean the filter element with clean water to remove trace contamination.
Natural water purification can also be achieved by leaving clarified water in a clear plastic bottle for an hour or two in direct sunlight as ultraviolet rays from the sun kill bacteria instantly.
If left alone, most sedimentary content of water will simply settle all on it's own, and the top layer can be skimmed or sucked off using a reed, straw or any tube for that matter.
Save that Tshirt, trooper! Use that as clothing, medical bandaging or something more suited. Personally, I don't believe in destroying any piece of your kit without absolute need. The point of training yourself to "professional" levels is to be able to accomplish a lot more than others using a lot less. There are several natural and widely available filtration media that would also offer added nutritional or medicinal benefit. Something to think about.
Here's why: Number one, usage of a tshirt as a filter material may work, but is highly ineffective as it is too porous, and may well be placing dissolved toxins from your skin and sweat or even deposited detergent remnants right into your drinking water. This may cause a number of intestinal distresses that lead to poisoning, dehydration and even death. Just depends on what you got on your shirt.
Nature was kind enough to provide a better solution with a little help from mankind. Also, if you are in a true E&E scenario or actual survival situation...you may not have all that kit, you may well be stuck with your EDC...better be able to endure either way. Save your kit for when your skills won't make the difference. In a SHTF scenario, you may well likely not be able to get back down to Bass Pro Shops for replacement filter elements and so on. Develop your primitive skill set and save the kit...can't stress this enough.
Here's another option:
As mankind is the worst littering thing there is, trash is generally not hard to find. A simple, functional and effective water filtration method that involves no cost and can easily be replaced is a simply pop bottle. Fill it with lightly compacted layers of grass, charcoal from your fire and sand. Dig down beneath the top soil to locate cleaner stuff.
The sand and grass will filter out most particulate matter and the charcoal will destroy any contamination. Boiling is actually not required, as it has been proven that you need only reach a temp of 180deg F to kill any organisms. Simply seeing the water boil is a visual indication that you have exceeded that temp. Additionally, if you are not interested in blowing stealth, not having a fire around might up those odds.
There are tons of other options, and while Franke's method here would work...if you are thinking about really being able to endure long-term, save the kit items. They might be hard to come by.
M