Looks like box turtle and bird pecking damage..testing for ripeness. Believe me, when your melons are ripe the scent will draw every critter in the neighborhood.
I learned to put each melon inside a pair of metal colanders and tie the colanders together. Keeps the melons off the ground and protects from most damage.

well, i wound up cutting that fruit off because another one set and it was the size of a marble and it had a web-like thing on it attached with a leaf from the plant (so basically the leaf was stuck to the marble sized fruit using the web as the sticking material) and i went to rip the web off and unstick the leaf and BAM! a caterpillar popped out of it and i cut that one also...i just decided that im going to let the plant grow for now i guess....until i get the bugs under control.

but thanks for your info.

Wow, dottie, what a great idea! I planted cataloupes this year for the first time. What a disaster. I got eight melons to set. Some kind of worms dug into most of them and ate/rotted out the centers. What the worms didn't get, the critters, did. Maybe chipmunks. They were watching them, evidently, and just as they were getting ripe, something would just rip the melons open and eat them, rind and all. I sure am grateful that I don't have to depend on my own garden 100% for food...:)

im thinking maybe next time i wont plant them in the ground, and ill plant them on the second. or third story of my house away from all the pests...