Delay when closing a window after starting a background process

This problem has been plaguing me for years now, and still now with
the recent 4.6.2 release.

Steps to reproduce:
1. Start a new screen session.
2. Create a new window.
3. Hit Ctrl-D. Window closes instantly.
4. Start another windows.
5. Run the following bash command: sleep 100 &
6. Hit Ctrl-D. Window will hang in dead state until you kill the sleep
process, or about 7-9 seconds elapse - whichever comes sooner.

I had a friend reproduce the problem on 4.6.2 in Arch Linux (I'm on
Ubuntu) and another reproduce it on 4.05.00 (Debian 9).

Any ideas?