Here's what turnitin says about their lengthy grading process:
If you access the GradeMark page in the document viewer (open the student's work in the document viewer and then ensure that you click on the word 'gradebook' towards the top left of the screen.) Insert the relevant grade in the top right of the screen for the student's work. This grade will automatically transfer to the GradeBook without the need for you to make a note of the grades.