This picture almost captures the sound Kate makes when she sees Tinker. It's a unique squeal of happiness, only heard when she is around the cat. Kate also says, "Kee-ee" to the cat. But in all honesty, she'll call the fridge "kee-ee" too.
Finally, I notice in looking at the pictures that Tinker is holding very still, facing the couch pillow. I think she's pouting, just barely tolerating the fact that we let Kate pet her. What Tinker is actually thinking, "Sure, I could get up and move. But I was here first, darn it! I was here first!"