Of course they have the right to grieve - if they didn't, that would be like telling someone who chose to have their pet euthanized (for whatever reasons) that they couldn't grieve because they chose to have the animal put down. Some women feel something like post-partum depression after an abortion, even if they're totally thrilled to be rid of the fetus they didn't want. A lot of these women think about the "what if" factors, like what would it be like if they kept their child? And they probably get told by at least one relative/friend/acquaintance that what they did was evil or immoral, or it was homicide, and this doesn't exactly make the woman feel better, and through a series of thoughts, the woman may develop a sense of regret, which leads her to carrying around ultrasound pictures in her purse, having a fake birth certificate made for the child, keeping the fetus next to her bed in a jar of formaldehyde, et cetera.
Despite feelings of sadness or guilt post-abortion, most women will admit at some point after the procedure that what they felt the most was relief. If they feel so awful about the choice they made, they have no one to blame but themselves because the choice was theirs an no one else's. Bed, made, lie...And then they move on.