Are you asking about placing a screen over the egg laying medium, just for the short time the females will be laying eggs? That's a great idea. We like to recycle, so I would recommend clean tights (hosiery) and a rubber band.
How many adult crickets will you have?
They will be ready to breed when the males are chirping the the girls have good long ovipositors sticking out their back end.
We have tried different methods for breeding crickets, and this one works best for us (though I realize you weren't asking for all this):
Take a small, medium, or large (depending on how many adults you have and what size bin they are living in) plastic container that is about 2-3 inches in height. Fill it with moist substrate (we use peat moss)- it should be moist enough to easily clump in your hand. And place this container in with you adult crickets. You may have to build a little "bridge" to the egg laying container so your girls will find it.
THE NEXT DAY remove the container, cover it with a very damp paper towel, and place it on a heating pad set on medium. Keep it on the heating pad for 6-7 days. Be sure to keep the paper towel moist by spraying it with a little spray bottle once a day (I do it before I got to bed at night). If the peat moss gets a little "fuzzy" don't worry. For some reason this fuzzy growth does not bother the baby crickets at all. If the peat moss surface begins to look at all dry, then lightly spray the peat moss itself. If the peat moss dries out, your cricket eggs will be no good.
The baby crickets should begin hatching out on day 8. For this reason, on day 7 you want to place the little egg container into a larger container, but still placed on the heating pad. Remember to be sure the paper towel and peat moss do not dry out.
On day 8 the egg container is ready to be placed in your baby cricket bin. I do keep my baby cricket bin on top of a heating pad in order to facilitate the hatching of all the eggs.
Once you see the crickets begin to hatch (day 8) there is something you can do so you can quickly recycle the egg container. But this is not necessarily necessary. But it will make things easier as the crickets grow larger, and also helps more of the baby crickets dig out of their egg laying container. This is what we do: Cut a piece of "plastic canvas" mesh the size of the top of your egg container. Place this canvas on top of your egg container and gently flip it over. (Do this while standing over your baby cricket's empty new bin.) Place the egg container and plastic canvas upside down into the bin. Now remove the egg container. Your peat moss will sit on the mesh, retaining its egg container shape. Now take a strip of paper and wrap it around the sides of the peat moss, encircling it, and tape it in place. Your egg container will be ready to use again, and your baby crickets will be able to hatch out of the top and the bottom of your peat moss. Place a damp lettuce (green leaf or other leafy green veg) over the peat moss to keep it moist while the babies are hatching out. Replace the lettuce leaf as necessary.
If you leave the container in with the adults they will eat the eggs, and eat the newborn babies, either way. Also, it is almost impossible to sort out the various cricket sizes you might need, if all your crickets are living together.
Here is also a good link with instructions:
http://www.anapsid.org/crickets.html#Materials