i use a magic eraser on my aerators, along with a small toothbrush sized scrub brush. Just when they are on the faucet, I don't think mine come off.

unscrew and soak in clr

That's the problem, most of those I have looked at do not unscrew.

I have emailed several manufacturers this morning asking about this issue.

That is crazy! How are you supposed to remove the rocks of scale that get in there if you can't unscrew them?

We had some old shower heads that did not unscrew. I put the CLR in a ziploc bag and used an electrician's tie to hold it in place and let them soak. It worked pretty well, just be mindful taking it down and don't spill it on yourself. I always held a larger bag outside the smaller one as I cut the strap just as insurance, but I did it several times and had no problems.

I don't get hard water deposits but this gunky slimy stuff that has to be rinsed out frequently. Neither vinegar nor CLR would take care of this, it needs to be manually rinsed off and I can't brush it from the outside because it is inside the strainer.
I have driven the people at Lowe's and Ferguson crazy trying to remove the aerators on their samples.

I agree. Trying to find a solution. Gross black gunk gets in the faucet and difficult to remove. The screens don't come off for cleaning.

In my experience, most screens do come off. The faucets had to be assembled and you should be able to disassemble most if not all of them. It just may require a little ingenuity. If you absolutely can not get the screen out, you should be able to at least remove the business end of the faucet and backflush and/or soak the screen that way. Many manufacturers have lifetime warranties on their products and I would not be reluctant to seek a replacement if I had a malfunctioning faucet that could not be dissassembled to clean off a screen.

modellie-

Thanks for the links. I've juryrigged little removal tools to do that in my home workshop, and didn't know I could easily order something.