This is a controlled component, so all mutation of the tree data structure will need to happen in the tree's parent component. Add a function in your node renderer (maybe after clicking a trash icon), that deletes the node from the tree state. The component will re-renderer and your node will be gone.

I was thinking of making a generic tree manager class to provide basic functions (move, rename, add, delete) for managing the tree data structure in the parent component. Maybe I'll call it "Arborist"!