The Blums, two brothers and a cousin, were Alsatian immigrants who operated one of Galveston's busiest wholesale distribution and commission brokerage businesses from the late 1860s until the mid-1890s. Houston architect Heiner used the long, three-story facade to firmly shape urban space along this block of Mechanic Street by outlining the ground floor with a continuous arcade of tall openings. In 1981, Cynthia and George Mitchell bought the big, dilapidated building and hired Ford, Powell and Carson of San Antonio to rehabilitate it externally while transforming it internally into a small hotel. To insert the number of rooms required for economical operation, a mansard-roofed fourth floor—which Heiner had designed when the building was expanded along Mechanic Street in 1882 but that had never been built—was belatedly added.

During the 1980s and 1990s Cynthia and George Mitchell bought other buildings on both sides of the street, rehabilitating them to contain auxiliary spaces serving the Tremont. Architecturally, the most notable of these ancillary buildings is the three-story John Berlorcher Building (1858–1859) at 2309–2315 Mechanic Street by builder James Brown with its attenuated sixteen-over-sixteen-paned sash windows.