That is pretty interesting that it starts in utero. Maybe building up the muscles so they are strong enough after being born?

Biologists have found that the reflex is significantly more frequent in infants of fur carrying primate species. It is theorized that the grasping reflex evolved as it is essential to survival in species, usually primates, where the young are carried in the fur. The infant's ability to grasp onto a mother's fur allows the mother to keep the infant with her while foraging for food or moving from one place to another. This is beneficial to the mother because she does not lose function of her limbs or mouth (as she would from oral carrying). Carrying the infant with the mother also gives a degree of safety to the infant, which it would not have if it were left in a nest or other location away from the mother. The grasp reflex also allows young individuals to have more developed food manipulation and dexterity skills. This suggests that the grasping reflex is vestigial in humans and in other non-fur carrying primates.

And it says you can reverse the grip by tickling the back or the side of the hand. Coochie coo!

Wiki - Palmer Gresp Reflex is the gripping reflex's English term.