Please note that this does contain spoilers of J.K. Rowling's newest short story, Ilvermorny School of Witchcraft and Wizardry, and of Harry Potter and the Order of the Phoenix.
I was rereading Harry Potter and the Order of the Phoenix earlier today, at which I made a discovery. In Chapter 16, Harry, Hermione, and Ron were meeting the first members of Dumbledore’s army at Hog’s Head. On page 336, the Hogwarts students that were entering the pub to join the army, where it says, “three Ravenclaw boys he [Harry] was pretty sure were called Anthony Goldstein, Michael Corner, and Terry Boot.”
I recognized the surname as the wizard boys that Isolt Sayre saved and raised in America in the Ilvermorny history found on Pottermore. Isolt, the founder of Ilvermorny, saved Webster and Chadwick Boot from a Hidebehind, at which they nearly died. And after healing the two boys, Isolt discovered they, too, were wizards. Since their parents were killed by the creature, Isolt raised them as her own. The Boot boys were pilgrims of when the Europeans were first settling in what would become America. Both Webster and Chadwick helped found Ilvermorny.
Found near the bottom of the story, found under Growth of the School, it states, “Webster Boot became what would now be known as an Auror for hire. While repatriating a particularly nasty Dark wizard to London, Webster met and fell in love with a young Scottish witch who was working at the Ministry of Magic. Thus did the Boot family return to its home country. Webster’s descendants would be educated at Hogwarts.”
It is unclear of when exactly Ilvermorny was built or what year Webster moved back to England, but it mentions that it was before America’s magical government, MACUSA, was formed. Earlier in the story, it mentions Seraphina Picquery was the president of MACUSA as early as 1920. (found under Ilvermorny Today). So, Webster had to have gone back to England several years before 1920.
Terry Boot had to have been at least a 3rd year to go to Hogsmeade, meaning he was at least 14, making him be born in 1981, considering the first book in the series takes place in 1991.
Looking at these facts, I believe that Terry is a descendant of Webster Boot, perhaps being around 4-5 generations apart.