Succot is a Harvest festival. During the festival we use the myrtle, palm, willow, and etrog to represent the four types of species that grow in Israel. This is also mentioned biblically. The time of Succot varies on our calendar but the past one was from September 29th to October 6th. Next year it will be from October 17th to the 24th.
However, I do not expect the Pilgrims to know what time of year it falls at because I doubt they would have known the Hebrew Calendar. I only expect them to know it as a harvest festival, which is exactly how it is mentioned outside of the example of the booths, which may very well have originally been what workers would stay in during the harvest. Considering they rejected so much of what they saw in England,
"To the Pilgrims, there were only two sacraments: baptism and the Lord's Supper. The other sacraments (Confession, Penance, Confirmation, Ordination, Marriage, Confession, Last Rites) of the Catholic and Anglican churches were inventions of man and were therefore not Holy. The Pilgrims opposed the mass, and considered marriage a civil affair (not a religious sacrament). The legitimacy of the pope, the saints, and the church hierarchy was rejected, as was the veneration of relics. Icons and religious symbols such as crosses, statues, stain-glass windows, fancy architecture, and other worldly manifestations of religion were rejected...
The Pilgrims did not celebrate religious holidays--Christmas and Easter being the prime examples. These holidays were invented by man to memorialize Jesus, and are not prescribed by the Bible and therefore cannot be Holy."
I find it very unlikely they would hold onto a pagan festival, and much more likely they would take something from the bible that was such a large part of their religion and holy to them.
I didn't expect to be actually arguing that this is what happened and was just looking for clarification, but now that I've looked at their religious position it seems much more likely. And just to clarify, I don't believe they learned about Succot from Jews, but just from the Bible. The Jews were expelled from England in 1290 and weren't allowed back until 1655. For timeline in England:
Edit: The biblical verse explaining the reason for the booths could be understood as something like, "This is the reason you dwell in temporary booths; because you dwelled in them in the desert. Not because you were working in the fields and needed a place for shade and rest." That is how it could be understood in a historical context, though it may be incorrect.