Jesuit influence on native life took place in the 17th and 18th centuries. Said influence included the obvious missionary work of conversion. Other influence included exchange of trade goods such as metal crucifixes and medals. Such Christian inspired goods are found in some abundance in 17th and 18th century Iroquois villages in upstate NY, to name one sphere of influence.
However, Jesuit influence did not include any influence on the production of stone tools by the natives.
In addition, Jesuit influence was not present for the ~14,000 years of native history preceding the 17th century.
Since there is absolutely no reason to conclude that the stone artifact presented in this thread was created in the 17th or 18th centuries, there is absolutely no reason to bring up the Jesuits in this thread at all. And even if it could be demonstrated that the tool was fashioned in the 1600's or 1700's, there would still be no reason to raise the topic of Jesuit influence on native life, since the artifact seen in this thread is a native creation, not a Jesuit creation.