Dr. `Abdul-Fattah Idrees, a professor of comparative jurisprudence, explains the Islamic ruling of this as follows:
Generally speaking, the pigeon is of the games prohibited to be hunted in the state of Ihram. However, if the killing was not intentional, there would not be any compensation, because the obligation of the compensation for hunting or killing games in the state of ihram will only apply if the killing was deliberate and intentional. Things are determined by intentions and purposes. Almighty Allah said: “…And there is no blame on you concerning that in which you made a mistake, but (concerning) that which your hearts do purposely (blame may rest on you)…” [Al-Ahzab: 5].
Thus Allah holds us accountable for what is determined and resolved in the heart to be made or done. Almighty Allah said concerning the obligation of compensation for killing games: “O you who believe! do not kill game while you are on pilgrimage, and whoever among you kills it intentionally, the compensation (of it) is the like of what he killed, from the cattle…” [Al-Ma’idah: 95]
In conclusion, a person in Ihram bears no sin for killing a pigeon unintentionally and he is also not obligated to pay any compensation.’