Hi,
I know of a Levenia Pilgrim who married a James Pittman. Their son, also named James Pittman was my grandfather. F
They are from the Bird cove/Flowers Cove area of the Northern peninsula.
I do believe these Pilgrims also have some Mi'kmaq relation, though I haven't been able to track back far enough to tell for sure. (oral family history-we grew up with the knowledge of native ancestry in relation to the Pilgrim name)