  Path integrals and the Wilsonian renormalization group provide two
complementary computational tools for investigating continuum approaches to
quantum gravity. The starting points of these constructions utilize a bare
action and a fixed point of the renormalization group flow, respectively. While
it is clear that there should be a connection between these ingredients, their
relation is far from trivial. This results in the so-called reconstruction
problem. In this work, we demonstrate that the map between these two
formulations does not generate non-localities at quadratic order in the
background curvature. At this level, the bare action in the path integral and
the fixed-point action obtained from the Wilsonian renormalization group differ
by local terms only. This conclusion does not apply to theories coming with a
physical ultraviolet cutoff or a fundamental non-locality scale.
