Most moths make very little noise on the screen, but the geckos, lunging at their prey and at each other, scritch on the screen and sometimes bang their heads on it. Some are pregnant females--you can see the eggs inside them clearly. Some are much smaller than the others (though I never see the new hatchlings, sometimes found in the house, on the screens at night.) Sometimes one catches a moth and doesn't gulp it down before another comes, grabs the other end, and they struggle with it. Around the edge of the window framing, gecko heads protrude into the light, just enough to look really weird (what IS that peering from the ivy? Oh, just another gecko.) When engaged in gecko-gecko interactions, they often do odd things with their tails--raising them and making snaky moves is the commonest. That frequently means that a big one is about to lunge at or chase a small one.
It's hard to think of Nature red in tooth and claw, with such funny little creatures as geckos on the windowscreen...except if you think about it from the perspective of the moth, beetle, or fly about to be snagged.