[Coda]

Birds can still fly if they're missing a few feathers. They lose them naturally all the time. (My cockatiel is managing to maintain nearly-level flight even with HALF his wing feathers missing right now!) The only real risk is that plucking out a healthy feather might cause an injury -- but that's less of a problem than keeping the mousetrap caught, so the pigeon is better off now than it was before.