I am just guessing now but I have often see Henthorne spelt with a very tightly closed "e" so that it looks like it is and "i". Could the name change be just simply a combination of poor writing and or spelling? Ot it could be due to the way it was pronounced locally and thus spelt differently.
In my own family history an "e" suddenly appears on the end of Henthorn a few generations back. I can see no reason for it other than thinking the wordlooks more rounded, finished off or some sort of snob value to doing it, otherwise why bother.