Here we have direction from the airport company that for a "possible" bird strike we will advise landing aircraft and continue operations until the runway can be inspected unless a pilot reports seeing something on the runway.
For a "confirmed" bird strike the surface is closed and must be inspected. No discretion.
Controllers and pilots should be allowed to use their discretion regarding bird strikes and other wildlife. Last night we received a phone call from the fire service watch room reporting a deer very close to the landing runway. A deer is much bigger than a bird so we suspended operations on that runway immediately. Only one aircraft missed the approach, all others were re-positioned to the parallel departure runway.