My water line broke, after fix, I ran water in the stationary tub to
clean out the line. But forgot that we had flushed the toilet while
the water was off. So when the water came back on, the tank began to
fill with the dirty water.
Now something (dirt/stone) is blocking the intake. The tank takes
about 30 minutes to fill. (The overflow pressure is fine, it is not
blocked.

How can I dissasemble this to clean it out? There are no screws on the
stop of the assembly. Just a solid blue plastic top on the valve
assembly. Does it screw off? Snap off? How do I remove the entire
assembly from the tank, if needed?

I'm not very knowledgeable, but willing to try anything to avoid the
expense and inconvenience of finding a plumber over the Thanksgivin(g
holiday.)