1) Feed one of the cats
a) Take 1 slab of poultry meat and go to Beeletun. Near the waypoint, walk around the green tent above the cat's head, in green, it says "cat". Feed it the slab of poultry meat.
b) Cook up 1 portion on Grilled Poultry and go to Lion's Arch. Go to Eastern Ward Waypoint. Head North East. The cat is near the lookout. Feed it the Grilled Poultry.
A dead bird will appear in you home instance. 5 days later a cat will be in your home instance. (Don't be concerned if it doesn't happen right away, a random amount of entering and leaving may be required.)