You decide whether to exile Greenwarden of Murasa as the last ability resolves. Players can respond to this ability triggering, but once it starts resolving and you decide to exile Greenwarden of Murasa, it's too late for anyone to respond.

If the target card becomes illegal before the last ability resolves, it won't resolve. You can't exile Greenwarden of Murasa in that case, even if you want to.