The correct answer is D) remind New England Puritans of their religious foundations.
The "half-way covenant" was created in the mid-1700s in order to remind New England Puritans of their religious foundations.
The Puritans adopted the half-way covenant to allow unconverted children to be baptized to become members of the church and with this, the possibility to have political rights. The covenant represented a kind of membership to church in New England by 1660. So yes, The "half-way covenant" was created in the mid-1700s in order to remind New England Puritans of their religious foundations.