Given that his mother was married to Benjamin Stratton as well as Henry Bagwell, I believe this is Benjamin's son instead of Henry's. Otherwise, wouldn't his name be Thomas Bagwell?
That said, Henry and Alice did have a son named Thomas, but the dates of births for the two Thomases are too far apart to be the same person, so I think they were half-brothers born from different marriages their mother had.
Of course, there is nothing in his profile About section except gedcom uploads, so there's nothing to shed any light on who was his actual father.
Any information anyone can add to help clarifiy would be appreciated.
Thanks