Yes, there is an enzyme specific to Green kiwifruit that causes allergic reactions with kiwifruit or food containing kiwi fruit in some people. Treatment depends on the nature and amount of the reaction including:

Dietary reformation and allergen avoidance: with education of children, parents and all the people.
No treatment: if signs are weak and self-limiting
Antihistamines: Useful for allergic rhinitis and some allergy mediated skin conditions
Also check with your doctor before trying it.