The reality is Kaworu adores Iskierka. He lets her perch on his head and sleep in his bed. She's a connection to someone that he misses so deeply and dearly that it eats away it him. His affection is evidenced by the notes and connecting screen have taken over and consumed his and Paul's room like a fungus.

The thing that he doesn't adore is when she tries to wake him up far too early (it's noon). He grumbles softly in his sleep and swats at her as she chirps and nibbles at his hair.