In the hanna test, if the filter is working properly, there is absolutely zero gray particles that survive the filtration step. That said, there are a lot of ways for the filter assembly to fail, apparently. My first time using it I accidentally discarded a clear plastic disc part that was stuck to the bottom of the paper filter, and after that the next paper filter tore and allowed particles through because it wasn't supported correctly. After fishing for the plastic disc in the trash, the issue was resolved!
Rick had much worse luck than me, no amount of troubleshooting ever got his filter holder assembly to stop leaking.