From The TimeSplitters Wiki

Strudel is Khallos's pet cat that is actually a robot. Strudel is mostly used for the Challenges in the Cat Racing section. Strudel is also found on the Khallos Express, where Khallos uses a switch under its head to activate the poison chamber. Strudel can be used in this level, but is just a pointless thing to mess around with. Strudel is also held by Khallos when he is being selected on the character select screen.

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