Can I move a backlog item out of a Kanban board?

Yes, you can unassign a backlog item from a Kanban board anytime you want, by dragging it back to the "Backlog items that are not assigned to any board" box to the left, or using the right-click menu.

When you do this, the progress of the item will be kept, and you can later assign it to the same Kanban board, another Kanban board, or a sprint, to continue working on it.

When you've completed a backlog item, archive it instead.