How do I unscrew the water filter cartridge holder?

I had the same problem with a Pur faucet attachment. I got one of those tools that unscrews the oil filter or some other part in a car. Its a metal strap on a handle and when you turn it, it tightens itself on the fulter. Or try using a scrap of padded grippy shelf liner and a large jar opener. I buy that liner by the roll at Costco and use it for dozens of things. I you don't have it use a rubber glove or shower mat. If the filter is small enough you can use channel lock pliers. Remember righty tighty, lefty loosey. So turn left to remove it.

I looked up what they are made of: The standard pitcher replacement filter is made of ion exchange resin and granular activated carbon. The PUR Plus Pitcher replacement filter contains ion exchange resin and granular activated carbon enclosed within a pleated microfilter. The microfilter allows for the removal of microbiological cysts such as Cryptosporidium and Giardi. The filter contains an antimicrobial agent to prolong the life of the filter. The contaminants or other substances removed or reduced by this unit are not necessarily in all users' water. In large scale systems, activated carbon can be rejuvenated by heating and ion exchange (the little plastic beads) can be rejuvenated by salt solutions. For example, my parents have an ion exchange unit that treats their well water and they have to add salt to a rejuvenating solution that backflushes (elutes) the column periodically. The microfilters are probably not easily cleaned and would have to be replaced, although pressurized back-flushing could extend the lifetime of these filters in a large system. The economics of scale with pitcher-sized units makes it uneconomical to perform any recycling so disposal seems about the only option. (I've worked on industrial and institutional sized water treatment systems over the past 15 years as part of my job). This is one of those dilemmas that seems to happen a lot when you try to do the right thing. You've ended up trading one waste product for another. The issue raised by the above web link that the filters are toxic time bombs is misleading. The level of contaminants captured from filtering a few hundred gallons of water is trivial. In fact, the presence of the adsorbing materials will fix contaminants present in the landfill leachate and help prevent their migrition into the natural environment. The problem with disposing filters is simply that you are tossing away a solid waste that really doesn't need to be disposed. I doubt that the filters placed in the recycling bins actually get recycled. I have been to several sorting facilities (I do a lot of environmental inspections) and non-recyclables are removed manually on a sorting line (It is really a terrible job I would think, picking through other people's trash all day long, and it smells). Anything removed from the line is sent to landfill.

Are you sure you are turning in the correct direction?

If the cartridge holder cylinders screw on to the bottom of a housing, looking from above the housing, you would turn the cylinders clockwise. (If you were to look at it from below the bottom of the cylinders, this would be the same as turning counter-clockwise.)

if it is an inline filter, it will have a set type screw, if it is a housing type it unscrews from the bottom, catch water with a towel. otherwise i can't help. good luck

You need a strap wrench.

I got one at harbor freight. Sears sells them.

It's a common tool you can find just about anywhere they sell good tools.