My first thought was to try to install some screen material - like they have in windows - somewhere in the drain area. This is just a stopgap measure. It would have to be the plastic or fiberglass type so it wouldn't rust. Eventually, this will clog up with debris. The way this drain is installed is totally wacky and doesn't make any sense. I would remove it and put it further outside the door. You could dig it all up and install a new drain grille a foot outside the door and have a piece of pvc coming off this and run it into the old drain. Patch it all up with some hydrolic cement (where the new pipe meets the old) and then put concrete over the messy hole so it drains down from your door to the new drain. THis way you don't have a hole in your house with water and bugs pouring in. THis really shouldn't be too tough. You might need help extending your door down but I would just raise the threshold, or get a new aluminum one, and make it part of a new "curb" that would help keep the water out.