From The TimeSplitters Wiki

Strudel, Khallos's pet cat, is actually a Robot. It most commonly appears in the Cat Racing Challenges. Strudel can also be found in the Khallos Express, when Khallos uses a button under its head to activate the missile. Strudel can be driven in this level, but it has no practical use in the level, other than entertainment. The robotic cat is also stroked by Khallos on the character select screen in TSFP, although on cat racing challenges he is on the character select screen as a playable character.

Strudel can be placed on Mapmaker maps, usually just for show, or it could be used for Story missions. There is also a Sample Map called Cat Racing Extreme, a virtual race track made just for Strudel.

Strudel is a humorous parody of the white cat that Ernst Stavro Blofeld (the inspiration for Khallos) is stroking in the James Bond films. Unlike Strudel, the cat in the films is a real cat and does not have secret buttons concealed anywhere.