Hi there,
Only the owner of the KittyCat may physically pick them up since they are attaching to your avatar and go into your inventory. This prevents other users from 'stealing' cats from others.
Other users can pet / play with your KittyCatS though! They just need to right click the cat & click the 'pet/play' option in the SL pie menu.
You can read more about interactions here (towards the bottom it goes over what other users can do with your cats) :
https://kittycats.ws/manual/article.php?id=64&oid=28
I hope this info helps. Feel free to reach out to me in world if you have any further questions or issues. Thanks