Looks like you need to replace the water heater.
It's the dip tube in pieces.
You may be able to flush all of that out of the water heater, maybe.
A few days ago, the water pressure dropped off considerably in my shower, and the tub fill became sluggish as well. None of the other plumbing fixtures in the house had any problems, although the water had been temporarily shut off and drained for some plumbing work, suspiciously on the same day the problems started. The shower and tub are fed from a Grohe 34 311 thermostatic valve. Since the pressure rose as I turned the temperature control colder, I figured that there might be some obstruction on the hot water side. So this morning I finally got around to taking apart the valve.
And what an obstruction I found! Crammed in the supply pipe, outside of the interior check valve, I found (and pulled out) perhaps a dozen strips of what looks like shaved plastic or scraped paint. In the pipe, of course, they were all scrunched up, but pulled out, the strips measure 5/16 to 7/16 wide, are 0.005 to 0.006 thick, and are an inch to several inches long. They have many holes througout, but many of the edges look fairly straightly cut.
What could this stuff be, and how did it get into my hot water supply line?
Many thanks for the reply. I had feared it might be something wrong with the water heater, which is 25 years old (1988) and will probably need to be replaced sooner rather than later anyways. I set about draining it, to see what else might come out, but much to my surprise, there was essentially no sediment of any sort. No more of the plastic-ish shreds, no sand, nothing. I didn't drain the whole tank, but it didn't seem like I would gain anything continuing to drain clear-running water.
The heater was made before that era in the 1990s when all the dip tubes were bad, and the strips I pulled out don't really look like the crumbling plastic bits one can see in a google search for "disintegrating dip tube". And so far still, no blockages at other hot water outlets, nor any problems with the hot water supply.
I'm going to hold off replacing the water heater for now, and generally treat this as a very strange one-off problem, until something similar happens again.
Is this on municipal water? If so, it could be PVC cuttings from a cut in. The HWT might be the first in line on the path of least resistance and so it collected it.
I suspect it's the water heater as well. At 25 years old, the heater has served you well, but it's time to replace it.