Hello,
I also had some bugs (thunderflies) entering 2 of my screens the same day, 5 years ago. Fortunately one screen was an expensive Iiyama, damaged a few days before the 3-years warranty period, so I could send it for repair. The other screen, in an Acer laptop, had the dead flies at the same place for the last 5 years. Fortunately they are located in the bottom taskbar and on the far right of the screen, so it is no so much disturbing.
Here is a tip it they still alive : press gently on the screen with your thumb, so that they are forced to walk towards the border of the screen, and when they are very close to the border, press strongly on the screen so that they are crushed. One of the flies first walked up to the center of the screen, but with this trick I was able to force it to go all the way back to the border...
Good luck !
metatech