According to the Scrum Guide1, the definition of "Done" is a formal description of the state of the Increment when it meets the quality measures required for the product. The definition guides the Development Team in creating a "Done" Increment. The definition of "Done" is created by the development organization (or Development Team if none is available from the development organization). The definition of "Done" may vary significantly per Scrum Team, depending on the context. One aspect of Scrum Teams inspecting how they work toward their Product Goal is that they improve their definition of "Done" over time. Therefore, if a Product Backlog item worked on during the Sprint does not meet the definition of "Done", two things that should happen with the undone Product Backlog item are:
Put it on the Product Backlog for the Product Owner to decide what to do with it, as they are accountable for effective Product Backlog management and ordering.
Do not include the item in the Increment this Sprint, as it does not meet the quality standards and may compromise value.
The other options are not appropriate, as they may compromise transparency, inspection, or adaptation.

The correct answer is B, because the Scrum Guide states that "the Development Team modifies the Sprint Backlog throughout the Sprint, and the Sprint Backlog emerges during the Sprint. This emergence occurs as the Development Team works through the plan and learns more about the work needed to achieve the Sprint Goal." Therefore, new work or further decomposition of work can be added to the Sprint Backlog as soon as possible after they are identified by the Development Team.