  Topological superfluid $^3$He, with unconventional spin-triplet p-wave
pairing, provides a model system for topological superconductors, which have
attracted significant interest through potential applications in topologically
protected quantum computing. In topological insulators and quantum Hall
systems, the surface/edge states, arising from bulk-surface correspondence and
the momentum space topology of the band structure, are robust. Here we
demonstrate that in topological superconductors the surface Andreev bound
states, which depend on the momentum space topology of the emergent order
parameter, are fragile with respect to the details of surface scattering. We
confine superfluid $^3$He within a cavity of height comparable to the Cooper
pair diameter. We precisely determine the superfluid transition temperature
$T_{\mathrm{c}}$ and the suppression of the superfluid energy gap, for
different scattering conditions tuned in situ, and compare to the predictions
of quasi-classical theory. We discover that surface magnetic scattering leads
to unexpectedly large suppression of $T_{\mathrm{c}}$, corresponding to an
increased density of low energy bound states.
