Katherine, don't know if this helps you at all, my grandfather was born Belfast 1903. His mother clearly was unmarried (she was the informant, the name given is her maiden surname, no father listed at all and the child was given her surname). The word 'formerly' was scored out in exactly the same way and I assumed it was because she was unmarried.
Can't advise about why Dunleavy is crossed out except as others have suggested, because she gave the father's name but was unmarried. Think I would contact the register office to see if there is any further information to be gleaned.