  We compute the response matrix for a tracer particle in a compressible fluid
with odd viscosity living on a two-dimensional surface. Unlike the
incompressible case, we find that an odd compressible fluid can produce an odd
lift force on a tracer particle. Using a "shell localization" formalism, we
provide analytic expressions for the drag and odd lift forces acting on the
tracer particle in a steady state and also at finite frequency. Importantly, we
find that the existence of an odd lift force in a steady state requires taking
into account the non-conservation of the fluid mass density due to the coupling
between the two-dimensional surface and the three-dimensional bulk fluid.
