When U.S. lawmakers enacted a new tax break to help low-income communities last year, backers said it would lift up some of the most distressed parts of the country.

But that wasn’t the pitch former White House spokesman Anthony Scaramucci used on Dec. 11 to recruit investors for a real estate investment trust that will seek to claim the tax incentives by investing in some of the nation’s newly created “opportunity zones.” Here’s how he described one of the REIT’s...