The only part of my paternal-side family tree left to deal with on the FamilySearch Family Tree is the maternal side of my paternal grandfather. The Bannons and the Hylands originated in County Laois, Ireland, and then left Ireland for Oldbury in England, before some of them left to come to Newark, New Jersey. After the Bannons and Hylands arrived in England, William Bannon and Mary Ann Hyland married (as did his sister and her brother).
William Bannon: https://www.familysearch.org/tree/person/details/KV1S-N8F
Mary Ann Hyland: https://www.familysearch.org/tree/person/details/KV1S-N8N
I couldn't find any duplicates for either, so I moved on to their parents (William Bannon and his wife Mary, and James Hyland and Catherine Delaney).
I couldn't find any evidence of William (the older) and his wife Mary in the FS Family Tree, so I added them:
William Bannon: https://www.familysearch.org/tree/person/details/GHBK-V8J
Finally, there are Mary Ann Hyland's parents, James Hyland and Catherine Delaney:
Catherine Delaney: https://www.familysearch.org/tree/person/research-help/GH3V-P53
And here is where things got a little tricky. Someone already had a James Hyland and a Catherine Delaney in the tree, but with a child in Wisconsin. This made no sense, as James and Catherine left County Laois (also known as Queen's County, Ireland) for England, but never came to the United States. So there is some confusion here. I disconnected that child from my James Hyland and Catherine Delaney (I suppose there could have been more than one couple with the same names).
And with that, at the end of Week 1, I completed cleaning up my paternal-side family on the FamilySearch Family Tree.