  Identifying the superconducting gap symmetry and topological signatures in
the putative spin-triplet superconductor $\text{UTe}_2$ is an important issue.
Especially, a smoking-gun detection scheme for Majorana surface states
hallmarking topological superconductivity in $\text{UTe}_2$ is still lacking.
In this study, we examine the surface spin susceptibility of $\text{UTe}_2$
with a particular focus on the contribution of the surface states. We find that
Majorana surface states contribute significantly to the surface spin
susceptibility, and give rise to an Ising-like anisotropy and anomalous
enhancement in the surface spin susceptibility. We calculate the surface spin
susceptibility as well as the local density of states using the recursive
Green's function method and examine the anisotropy of the surface spin
susceptibility in terms of the topological surface states and symmetry for all
irreducible representations of odd-parity pairing states. Our results indicate
that the Ising anisotropy and the anomalous enhancement are attributed to the
Majorana surface state protected by the crystalline symmetry. These findings
suggest the possibility of detecting the Majorana surface state via magnetic
measurements.
