You have to detach it from the sink. Disconnect the discharge hose, unplug the power cord, and work on it outside the sink. It’s a god idea to preorder the splash guard first, so the sink is not out of commission for long.
This problem is usually 99% a clogged vent hose. A lot of times they get kinked between the dryer and the wall. How sure are you that it’s clear? If so, sometimes, you can snake a vacuum cleaner hose into the lint collection hole and clean it out. Otherwise, disconnect the vent hose from the back or side of the dryer, and vacuum out the lint from there.
Tap it with your finger, in case there’s a chip caught. Also, try using a hair blower in the opening, to possibly melt a piece if jamming ice. Dispense ice, and watch the door action. Does it stop at the same place every time? If so, the retractor mechanism might be broken. Find disassembly instructions on U-Tube.
The control knob is attached to a clockwork timer. The mechanism is probably worn. Sometimes you can find a used timer at an appliance repair shop, which I did. Otherwise order on line. They’re easy to replace. Look on u-tube.
It could also be a washer in the shut off valve downstream from the ice maker. Washers eventually disintegrate, and the sediment will end up in the ice. If it's rubber or neoprene pieces, they are harmless. Proving what it is, or where it came from is difficult. Do you know anybody in a lab who can analyze the specks? You could also put a small in-line filter in the 1/4" feed line to the fridge.