Which hook is invoked when pressing the remove button with widget image?
This message is coming from node_form_submit.
That function subsequently calls node_save which in turn calls the following hooks:

// Let modules modify the node before it is saved to the database.
module_invoke_all('node_presave', $node);
module_invoke_all('entity_presave', $node, 'node');
...
module_invoke_all('node_' . $op, $node);
module_invoke_all('entity_' . $op, $node, 'node');


where $op is one of 'update' or 'insert'.