The Product Owner should care that the Scrum Team adheres to its Definition of Done because:

It helps to forecast the team’s productivity over time. By having a clear and consistent Definition of Done, the Product Owner can measure the amount of work that the team can deliver in each Sprint and plan accordingly.

It affects the product’s total cost of ownership. By ensuring that the work done by the team meets the quality standards and expectations of the stakeholders, the Product Owner can reduce the risk of technical debt, rework, defects, and maintenance costs in the future.

References:

Scrum Guide 2020, page 10: “The Definition of Done is a formal description of the state of the Increment when it meets the quality measures required for the product.”

Scrum Guide 2020, page 11: “The Product Owner is accountable for effective Product Backlog management, which includes … ordering Product Backlog items; and, ensuring that the Product Backlog is transparent, visible and understood.”

Scrum Guide 2020, page 14: “The Definition of Done creates transparency by providing everyone a shared understanding of what work was completed as part of the Increment. If a Product Backlog item does not meet the Definition of Done, it cannot be released or even presented at the Sprint Review. Instead, it returns to the Product Backlog for future consideration.”