I think this is reasonable and probably how we would handle it.I guess it would depend on what kind of relationship you have with your neighbor. If you're comfortable in talking to them about the incident, to find out what kind of assurances they will make to prevent it form happening again, I'd do that to preserve the neighborly vibe. If not, ask a neighbor to do it. If not then, report the incident to animal control. Animal control should approach them either by letter or in person to tell them the incident was reported anonymously.
Hope little Gizmo heals up quickly.