My understanding is that the itch of mosquito bites is a histamine reaction, similar to hives or other allergies. That's why caladryl lotion applied topically helps; it contains benedryl, an antihistamine.

Because I have seasonal pollen allergies (hay fever), I take antihistamine pills regularly all through the spring and summer. One unexpected side benefit is that the mosquito bites I get don't result in itchy red bumps. I barely notice them.