About halfway through the story, Mr. Woodifield tells his friend, known as "the boss," that "the girls were in Belgium last week having a look at poor Reggie's grave." The "girls" that he refers to here are his wife and daughters, and "poor Reggie" is his son. Mr. Woodifield's wife and daughters were in Belgium visiting Reggie's grave.
Mr. Woodifield also says that his wife and daughters were "delighted with the way the place is kept," the "place" here being the graveyard. Describing this graveyard, Mr. Woodifield says that "There's miles of it ... and it's all as neat as a garden." The implication here is that this is a graveyard for soldiers who have been killed in war. Often these graveyards comprise lots of white crosses in neat and ordered rows. The grass in these graveyards, as a mark of respect, is likewise kept very trim and neat, as Mr. Woodifield describes.
"The Fly" was first published in 1922, so the war in which Reggie was killed was most likely World War I. Many fathers at this time would be grieving for the loss of sons who died in the war. Indeed, "The Fly" is mostly about the grief of the main character in the story, known simply as "the boss." This character seems to have been affected much more severely by the death of his son than Mr. Woodifield has been by the death of his. The suggestion in the story is that both sons died in the same war.