The delegation approached the King and Queen to ask for protection under Muggle law. Many see the failure of this mission as one of the prime motivating factors behind the Statute of Secrecy.
William and Mary began their co-regency in 1689, the same year that work began drafting the Statute of Secrecy. This strongly suggests that the mission to appeal to the British monarchs occurred very shortly after they ascended to the throne. The Statute of Secrecy actually went into effect in 1692, which means that the mission predated that event. For the purposes of this timeline, then, we'll place the year of the mission at approximately 1690.