Going back through my sources, I think we may need to cut her parents entirely. Her being the daughter of a William Thompson was something gleaned from Roxbury records, but that database linked in the "About" is no longer accessible and I can't find a reference to her birth surname or father anywhere else. Since I can't replicate that research, and since the other cited sources give no known birth surname, I don't think I can stand by that assertion. All we can verify at this point is that she was named Rebecca, she was born in 1613 in England, and she married John Gibson.
We also have in the profile that she immigrated in 1633 with both her parents, but I'm not finding a Rebecca Thompson in manifests for that year. Perhaps someone else might have better luck?