I just spoke to Wirral Record Office. They told me the certificate they would provide would be exactly the same as the one I had already ordered from GRO.

She pulled up the certificate whilst I was online and confirmed everything ie Eleanor Crowe, domestic servant and that Father's name (Thomas Shields) was crossed out - she said this could either be a genuine mistake by the registrar or that Eleanor requested it be crossed out. But I'm afraid we'll never know.