The grass clippings are coming in through the tolerances in between the air filter and the tube it slides onto.. or the male/female connections of the air filter. the paper element media is filtering everything
I’m not sure what you’re describing here but I believe that you have some type of plastic canister that holds a cylindrical paper filter that is open on both ends. One end may be closed except for one hole that attaches it to the canister.
The air is pull into the plastic canister and moves around the annular space between the plastic and paper filter. The paper filter should be sealed against the plastic housing at the front and rear ends so all air should flow freely through the paper filter and any large pieces should remain on the outside of the paper filter. Large particles may get lodged in the back end of the annular space outside the paper filter. When removing the paper filter those large particles can then fall into the clean inner part of the paper filter area.
If a large particle gets past the paper filter then it will get sucked into the engine as far as I know. Is there some mesh at the inner end of the plastic housing?
If the paper filter was not installed properly then maybe something could be lodged into the unsealed space at the ends of the filter.
Please describe what you mean in better detail.