The cat harness is a quest item in The Witcher which is the goal of the Small Problems quest. It has been stolen from the "good" Griggs by rival Griggs (presumably, bad ones) and it is up to Geralt to retrieve it. This information is given to Geralt either by Abigail or the healer, depending on Abigail's fate in the Outskirts.
Once Geralt returns the harness. The Griggs are appeased and offer a four-leaf clover in return.