When a manager approves a rep's challenge and re-edits the goal and approves it again, the manager edit goal is not updated. But, when a manager clicks the Save button after the edited goal and approves it, the goal value can update correctly.
This is the expected behavior. The Approve button is there to only approve rep challenges, not to save manager edits. Managers, who need to make edits, need to click Save because this triggers additional validation rules. It is unnecessary if they are only approving a challenge.
CRM Help Documentation: Integrated Territory Feedback