Mine doesn't have the screen, seems like a plus that yours has it. I'm sure you can clean it out with some carb cleaner. I would take off that o-ring before spraying it, though I'm sure you are replacing it with new ones as part of the rebuild.
The fuel flows through the mesh screen you are asking about, into the center of the barrel, then depending the position of the piston determines how much fuel flows through each one of those elongated ovals.
Here's a good video on the rebuild process:
https://www.youtube.com/watch?v=BVFu5bCKkmA