"Fish?" Oh dear, she hopes that clutch recognized the presence of food and sorted it properly, where it would not spoil. There is some complex magic on her clutch. And someone else using it -- without knowing about the magic -- might wreck her whole organization.

"Here..." Hermione holds out a rune (the one symbolizing cat) to the cat demon. "I have to retrieve my wand before I can take items out of my clutch. By holding onto this rune, I will be able to find you afterwards. And give you the fish that is yours."