View the place (inaturalist.org/places/place-name) and at the bottom right of the map is the option to edit.
On the resulting edit page you need to “Edit layers” (the pen in a box symbol on the left side of the map) and then you can move the vertex markers, or create new vertices by dragging the midline markers.
Choose save (on the map next to the pen in box symbol) to save the layer
Then choose save at the bottom of the page to save the place.
It will take you back to the view place page. Don’t be alarmed that the map still shows the old polyline(s), because the display is probably cached. You can check to make sure it is saved correctly simply by changing the zoom level to one that hasn’t been viewed yet, so that it needs to redraw…
@kueda the “bug” where the map still shows the pre-edit shape is still in play… when I tested this just now, zooming to a couple other levels before doing the edit makes it so that those zoom levels are also affected once you return.