  The spacetime surrounding compact objects such as neutron stars and black
holes provides an excellent place to study gravity in the strong, non-linear,
dynamical regime. Here, the effects of strong curvature can leave their imprint
on observables which we may use to study gravity. Recently, NICER provided a
mass and radius measurement of an isolated neutron star using x-rays, while
LIGO/Virgo measured the tidal deformability of neutron stars through
gravitational waves. These measurements can be used to test the relation
between the tidal deformability and compactness of neutron stars that are known
to be universal in general relativity. Here, we take (shift-symmetric)
scalar-Gauss-Bonnet gravity (motivated by a low-energy effective theory of a
string theory) as an example and study whether one can apply the NICER and
LIGO/Virgo measurements to the universal relation to test the theory. To do so,
this paper is mostly devoted on theoretically constructing tidally-deformed
neutron star solutions in this theory perturbatively and calculate the tidal
deformability for the first time. We find that the relation between the tidal
deformability and compactness remains to be mostly universal for a fixed
dimensionless coupling constant of the theory though the relation is different
from the one in general relativity. We also present a universal relation
between the tidal deformability \textbf{of} one neutron star and the
compactness for another neutron star that can be directly applied to
observations by LIGO/Virgo and NICER. For the equations of state considered in
this paper, it is still inconclusive whether one can place a meaningful bounds
on scalar Gauss-Bonnet gravity with the new universal relations. However, we
found a new bound from the mass measurement of the pulsar J0740+6620 that is
comparable to other existing bounds from black hole observations.
