I'm suspicious of the "pill" like shape.....too hard for me to imagine that anything in the lines would take on that shape rather than a curved shape.
My vote is for a manufactured product, either chlorine with CA+/CYA or those CYA pucks.
Easy enough to determine if it is stabilizer or chlorine sticks. Get a 5 gallon bucket and fill it with tap water. Crush up one of the large chunks and put it in the bucket of water. Stir the water with a stick. Test for chlorine. If there is no chlorine test for CYA.
I would also ask the pool company exactly what products they have been using in your pool. I do know its not plaster. The pebbles would have been mixed into the plaster before it was applied to the pool, and reputable plasterers cover all the pipes to make sure no plaster gets in. Its not gunnite either. Gunnite has a much rougher texture. Sidewalk chalk would have dissolved and it wouldn't be one color on the outside and a different color on the inside.
I also vote for someone chucking something into your pool.
I got smaller versions of these up to two years after my pool was finished. It eventually stopped but it was plaster inside the pipes that eventually came out of the pipes. It eventually stopped but it was determined to be plaster for me.
SilkGuard Complete upgrades pool care by providing better all-around performance - with work on all pool types, with all pumps and in all applications. The compound action blue SilkGuard chlorine sticks kill bacteria, prevents algae, prevents metal staining and corrosion, reduces scale formation...
My water tested positive for copper when we opened this spring and I had no idea how it could have gotten in there. Doing some internet detective work identified the source - those helpful all-in-one sticks. Thank goodness I flipped over to TFP while my copper was only 0.3 - just below the level where blonde hair faces a risk of turning green.
I totally agree that this "debris" is left over construction / plaster that settled in the pipe(s). That explains the color and shape. One side has the half moon curvature. Just took some time to break it loose and travel to the basket.
Ok, for some reason viewing pics on my phone, I thought the debris was in the skimmer baskets and not the pump basket...my error. If that is the case, then these are definitely plaster pieces...there's no way anything of that size could be sucked into the drains., then the pump basket.
The OP said she was vacuuming via skimmer [that would cause a suction to pull the debris thru pipes and into pump basket. Anything dumped into the pool or skimmer baskets by pool guy would not be transported into pump basket unless they vacuumed too....pucks don't break that easy and neither does gunite, but saturated plaster would,,,,my only reservation is the quantity of the debris...that's A LOT of residual material in the pipes...I had one or 2 chunks that finally ended up in my scupper pump basket...it was also the color of my pebble tec. Has the OP stated what color is the plaster? If the same or near color, that's the material...