Claire Freemantle gets every mention of her name removed from the internet
She doesn't, because there are countless mentions of her on the internet.
What I'm sure she does do is have potentially false, misleading or defamatory statements relating to her zapped. Unlike the majority of us, she has the resources to do so reasonably effectively.
It's possible she's been granted a super injunction to prevent the publication of her picture. Again, she's in the rare position of having the resources.
Whatever the truth of the matter, it has obviously had, and will continue to have, a life changing impact on her and those close to her. In such a situation, I expect any of us with sufficient resources would take similar steps to minimize that impact.