An exotic linearised theory of superconformal gravity in D=6,(4,0) superspace, proposed by C Hull, is discussed in loop space with focus on its bosonic sector. Pursuing an analogy to the loop space version the system of a two form B and its field strength H, we show that the exotic linearised gravitational potential C and curvature G can be reinterpreted as an ultra-local (linearised) metric and curvature on loop space.