Among unconventional superconductors, UTe2 stands out for its extraordinary behavior: it regains its superconducting state at ultra-high magnetic fields above 40 tesla, after initially being suppressed around 10 tesla–a phenomenon known as re-entrant superconductivity. One proposed explanation involves transverse fluctuations of a ferromagnetic order parameter. Yet, UTe2 shows no clear signs of ferromagnetic order or strong fluctuations in standard magnetization measurements. To probe deeper, we measured the transverse magnetic susceptibility in pulsed magnetic fields up to 60 tesla. In a manner reminiscent of the transverse field Ising model, large external magnetic fields applied along the c-axis lead to a huge increase in the transverse susceptibility–over 30 times greater than the longitudinal response. These findings suggest that the highly-unusual, magnetic field-enhanced superconductivity of UTe2 is closely linked to this anisotropic magnetic response.