Inner cover screen?

My inner covers are also notched so the bees can use it as an upper entrance with the outer cover pushed forward. I've never had any comb built in that space.
Screening that over would remove the option of the upper entrance, but shouldn't "hurt" otherwise.

The hole in the top of the inner cover was to use the inner cover with a Porter Bee Escape to clear bees from the supers. The hole can be closed with no damage to the bees or their ability to vent the hive. In todays beekeeping the hole is most often used to feed the colony from the top with feed buckets.

I have never seen bees build in the space between the inner cover and the telescoping lid. You can skip adding the screen.

If bees are building comb on the top side of the inner cover, they are most likely out of storage space. Need to add a super. Removing a few full frames of honey and adding some blank foundation will help for a short period.

Screening the hole is likely to cause trouble with small hive beetle, ants, etc. Bees cannot patrol the cavity to keep the pest at bay and they can have a field day.