Correct spelling: irretrievably
in an irretrievable manner; " it is irretrievably lost"
But is your father's property so irretrievably involved, that you may not hope to recover it? - "The Prime Minister", W.H.G. Kingston.
She tried to remember the two or three names Mrs. Stanwood had uttered in a similar connection- but they were gone, irretrievably gone from her memory. - "Jane Oglander", Marie Belloc Lowndes.
Martin is, therefore, utterly, irretrievably ruined. - "The Martins Of Cro' Martin, Vol. II (of II)", Charles James Lever.