  Take a sequence of contactomorphisms of a contact three-manifold that
$C^0$-converges to a homeomorphism. If the images of a Legendrian knot limit to
a smooth knot under this sequence, we show that it is Legendrian. We prove this
by establishing that, on one hand, non-Legendrian knots admit a type of
contact-squeezing onto transverse knots while, on the other, Legendrian knots
do not admit such a squeezing. The non-trivial input from contact topology that
is needed is (a local version of) the Thurston--Bennequin inequality.
