  The gauge redundancy of quantum gravity makes the definition of local
operators ambiguous, as they depend on the choice of gauge or on a
`gravitational dressing' analogous to a choice of Wilson line attachments.
Recent work identified exact AdS$_3$ proto-fields by fixing to a
Fefferman-Graham gauge. Here we extend that work and define proto-fields with
general gravitational dressing. We first study bulk fields charged under a
$U(1)$ Chern-Simons gauge theory as an illustrative warm-up, and then
generalize the results to gravity. As an application, we compute a
gravitational loop correction to the bulk-boundary correlator in the background
of a black hole microstate, and then verify this calculation using a newly
adapted recursion relation. Branch points at the Euclidean horizon are present
in the $1/c$ corrections to semiclassical correlators.
