Yes, status-healing magic will work on the mosquito marks.

Moonwater will also get rid of the mosquito marks and their effects. However, it is illegal to collect moonwater for later use as it is a biohazard to Prismals. The Prismatican customs are incredibly strict about this! All containers with moonwater, hidden or otherwise, will be chucked into a waste disposal before you board the ship to the government center — much like how airport security will casually toss out your bottled water.