Additionally, if you want to move a card from one parent to another (rather than just removing it), you can use the drag-and-drop feature for that. Just start by dragging the child card’s title, then hold down shift while dragging, which enables “move mode”. Now when you drop the card onto a new parent card’s title (this can be anywhere in the interface where you can see the parent’s title, e.g. the noteboard, the outline, the backlink section, etc), it will remove any existing parents and add it to the new parent.
You can see a GIF of this in action here.
This would probably be ideal for your use-case, where you want to move cards out of “Inbox” into somewhere else in your structure.