Cheshire cats were known for their grins and their propensity to disappear.
When Biroc left while having a conversation with the Fourth Doctor, the Doctor said it was like talking to "a Cheshire cat". (TV: Warriors' Gate)
Bernice Summerfield, while losing consciousness, saw Carrefour's teeth slowly vanish "like those of a demonic Cheshire cat". (PROSE: White Darkness) The "Chesire Cat grin creasing her features into a deranged caricature" was an outward sign that Claire had been possessed by the Yssgaroth; however, later during the same Yssgaroth incursion in York, Xanara Pasam's own lips "widened into a Cheshire Cat grin" on a much more innocent occasion, namely her realisation that she had found a place where she could get some food. (PROSE: Night of the Yssgaroth [+]James Hornby, SIGNET (Arcbeatle Press, 2023).) Hervy, the Hervoken pumpkin which menaced Aoife Fitzgerald's household began smiling "a perfect Cheshire Cat grin" the more influence it got over her daughter Norah. (PROSE: Hervoken Halloween [+]James Hornby, Horrors of Arcbeatle (SIGNET, Arcbeatle Press, 2023).)
There existed an individual known as "the" Cheshire Cat , whom Iris Wildthyme encountered. (PROSE: Iris Wildthyme and the Polythene Terror) While visiting Wonderland, Iris and Panda had previously confused the Salford Cat for a Cheshire cat, only to be told that a Salford cat was "something else entirely". (AUDIO: Iris Wildthyme and the Land of Wonder) The Cat, a virtual being created by the Doctor's TARDIS to help the Eighth Doctor recover from the influence of Zagreus, was patterned after the Cheshire Cat as depicted in Alice in Wonderland. (AUDIO: Zagreus)