@Jobu28
I had an eel a long time ago who had escaped often. They are really strong, so even with a screen cover I'd suggest securing it with something like velcro.
When it does escape on you, be aware that with the think slime coat that they have (they are scaleless, so they have more slime coating then most other fish) will keep them alive outside of the water for hours. It is pretty amazing really. Grab the eel and place it back in the tank and give it 24 hours w/out messing with it, it will likely return to normal behavior. Once mine got out sometime during the day hours and I didn't find it until the evening and round it behind the tank covered in dust bunnies, back in the tank it went dust and all, and it ended up being fine.
Have you taken care of eels before? If not, I have other advice I can share w/you. I used to feed wild eels as part of a science center educational experience. Just let me know.