Is it permissible for a father to marry off his granddaughter without the permission of her guardian?

The grandfather of the girl from her mother's side is not her guardian (wali), so he is not permitted to marry her off, whether with her permission or without it. This is because the guardianship of marriage belongs first to the father, and then transfers to the most rightful guardians in order. A marriage conducted without a legal guardian is invalid according to the majority of scholars.