Toilet gunk from clean water hole
Sounds like deterioration of major rubber stuff, so get a plumber to entirely replace ALL of the toilet's components. Noticeable chunks typically indicate your tank gasket is going quick &amp; not just the tank needing to be cleaned. These particles can collect &amp; clog the toilet's functions if not addressed.

This requires removing the tank &amp; you may as well replace the bolts, their washers, the flapper &amp; the fill valve along with the new tank gasket. Probably $400 in parts &amp; labor for a Handyman or Journeyman Plumber ($20-$30 if you do it) &amp; good for at least a decade, so consider doing all toilets to ensure all water wasting is stopped.

However, getting a new toilet(s), that may work vastly better, might be the same Pro price &amp; of course would fix the gunk problem. So, ask the Pro about this option as a quicker &amp; better alternative. Lowe's cheapest Project Source toilets ($100-$130) were wonderfully welcomed replacements for my place when I did them.