Hotel brands and third-party operators are leaning on a previously obscure tool known as key money to boost their capital stacks in a sluggish hospitality real estate market. Key money is an up-front, forgivable loan that a brand, like Hyatt Hotels Corp. or Marriott International, or a third-party operator offers to a developer or hotel owner to lock in franchise and management deals. It has become a common bargaining chip, helping owners bridge financing gaps, offset renovation costs and justify conversions that otherwise wouldn’t pencil. But the payoff isn’t uniform: Some owners say the funding is essential to making deals work, while...