The eight-year-old's costume caught fire while she was out trick-or-treating in London with her mum, and was consequently hospitalised with severe burns.
Claudia had been replaced by Zoe Ball who presents Strictly's spin-off show It Takes Two.
At the time Claudia and her family released a statement which read: "Our daughter was involved in an accident on Friday night while celebrating Halloween. She is having the best care possible and we are hopeful of a full recovery.
"We would like to thank everyone that has been so supportive and particularly NHS doctors, nurses and staff who have been absolutely incredible.
However Zoe proved a Twitter sensation when she joined Tess three weeks ago, with one viewer tweeting: "Zoe Ball should have this gig every week".
Another commented: "Totally chuffed for @ZoeTheBall getting loads of love for her stint on Strictly. Effortlessly cool & funny, she should be on the telly more."