The story is probably "Expedition" by Anthony Boucher.
Spoilers follow, don't read if you can access the story in the link in user14111's answer and read the story.
I remember this story. The Insect like aliens were Martian scouts, and the story is told in various messages they send. The human character tricks them into thinking Earth is too dangerous to invade, but their superiors see through the trick, and the aliens decide to build a base on the far side of the moon while they plan their invasion of Earth.
The human character is a man, and the Martians observe that according to the photos he shows, Earth females never wear any clothing. When the human character learns they were Martians he exclaims "Orson Welles!", so the story was written after the War of the Worlds Martian invasion broadcast on October 30, 1938. The first Earth images of the far side of the Moon were obtained in 1959, so the story should have been written between 1938 and 1959.
I think that the story is "Expedition" by Anthony Boucher, first published in Thrilling Wonder Stories August 1943.
Here is a link to a list of places where "Expedition" was published:
I probably read "Expedition" in a paperback version of The Best of Science Fiction, ed. by Groff Conklin, 1946.