I just saw a show about the origins of Thanksgiving on the History Channel the other night. My memory's not great, but they seemed to find historical, religious, and retail origins of the holiday. Supposedly, the first Thanksgiving was in 1621 (I think) and there exists only one document of the event which was lost for over 200 years. So in the meantime, there was no Thanksgiving. Its resurrection had something to do Christianity and its calendar date was purposefully placed to mark the beginning of the Christmas shopping season. FDR tried to move it soon after The Great Depression to the third Thursday of November to give retailers some extra early business, but that didn't work out.
As far as the initial event, there was no recorded invitation given by the Pilgrims, but there was record of a shared feast. I don't know how accurate the History Channel is and I was never very good at history, but that's what I've learned. I usually prefer to stick to math and science. 