Destry is a small commune in the Moselle region not far from Metz. This may be the origin of the surname, which shows up in French records as far back as 1606.
Other 17th-century spellings are d'Estree and D'Estrie, which makes me think it's probably related to the French word for east, and isn't connected with destrier, which is an Old French Latin-derived term for a warhorse.