The plugs should be left in to prevent ingress of dust, moisture, and dirt. I have similar plugs in dry compartments on my dozer and include inspecting them as a regular maintenance item every 50 hours. You could also install a wire gauze filter, but that would run the risk of being knocked off.
A hole that small will plug up with the first hint of 80w/90 gear oil and a little bit of dust. It’s just sound practice to pull the plugs periodically for inspection, and while you’re under there do a visual inspection for loose nuts and bolts. It’s responsible ownership.