Maybe every once in a while it would be worth checking the screen; but, its much quicker to just pour the oil out. I usually make less of a mess just pouring it out vs taking it apart anyway.
This is what I used,
Permatex® Ultra Blue® Multipurpose RTV Silicone Gasket Maker I got it at Advance Auto if I recall correctly, odds are AutoZone has it as well. I went with this as my mechanic buddy says it's the best (so hearsay); but, it requires 24 hours to dry before you are supposed to use it (run the car). He uses something else most of the time that dries up quicker. I also went with this since it's a gasket "maker" instead of sealer; it should be better at sealing gaps.
I was looking back at the pictures I took and was wondering the same thing; but, I believe I was concerned about getting gasket maker on the screen/anywhere it could get sucked into the intake/turbo. With only having gasket maker on the outside/up against the green gasket, it's held up at least 8 months without any oil leaks.
Good luck!