What document urged the king to acknowledge colonial grievances and restore rights while recognizing Parliament's authority?

The correct answer is indeed the Olive Branch Petition. This document was drafted in July 1775 by the Continental Congress and sent to King George III as an appeal to restore harmony between Britain and the colonies. The Olive Branch Petition sought to address the colonies' grievances and called for the recognition of their rights while still acknowledging Parliament's authority and England's sovereignty over the colonies. It was an attempt to avoid outright war by expressing a desire for peace and reconciliation.

The Declaration of Independence, by contrast, formally declared the colonies' separation from Britain and did not appeal for the restoration of rights; rather, it listed the colonies' grievances against the king. The Declaration of Rights and Grievances, while it did outline colonial rights and grievances, was not a direct appeal to the king in the same manner as the Olive Branch Petition. The Declaration of Causes and Necessities for Taking Up Arms was issued later in 1775 and justified the colonies' decision to take up arms against British authority rather than seeking negotiation.