Claire's composure made a lot more sense, knowing she dealt with constant emergencies as a career. So she probably saw a lot worse regularly than somebody bleeding on her couch. That she did that as a day job, and was still willing to put up with heroes showing up in shambles on her doorstep deserved a lot of respect. Claire was her own kind of superhero.
"The tattoo is a physical manifestation of my chi- um, that's your lifeforce, everyone and every thing has chi. It's energy. Anyone can learn to manipulate it, but mine's super charged with a kind of magical lifeforce energy I got from uh-" This probably wasn't the best time to drop a bombshell like ancient mystical dragon from a mysterious extradimensional realm inhabited by immortals. There was only so much you could expect a person to believe. "A thing," he finished lamely, but recovered by answering her next question with an amused snort and shake of his head."Close. I'm actually called Iron Fist. It's this whole legacy." More of the whole magical other-world thing he didn't want to scare her with.