  As a possible alternative to black holes, horizonless compact objects have
significant implications for gravitational-wave physics. In this work, we
utilize the standard linearized theory of general relativity to calculate the
quadrupolar tidal Love numbers of a nonexotic compact object with a thin shell
proposed by Rosa and Pi\c{c}arra. It is found that both types of tidal Love
numbers are positive and increase with the initial radius for almost all values
of the compactness parameter. Furthermore, they have an unexpected upper bound
and vanish in the most compact configurations. As a result, this model is
indeed a suitable mimicker of a black hole. However, we also observed that the
speed of sound within the fluid on the shell diverges in the black hole limit.
