Unfortunately, TurnItIn (still) doesn’t have the possibility that it regulates that 1 group can only hand in 1 paper (like a ‘regular’ Blackboard-assignment has). They say they are working on it, so hopefully in the next release.
One student hands in document and use “TII assignment by groups”
So you will need to ask the students that only 1 person per group hands in the document in TurnItIn. By using ‘Course Tools’, ‘TurnItIn assignment by groups’ and then click on the appropriate assignment and select the group, you will be able to see WHO and IF that group has submitted a document. And you can directly go to the Originality Report.
Grading via Blackboard assignment?
So, at the moment, you cannot use TurnItIn for grading groups via the grade centre (so that all the students of the same group receive the same grade). That is only possible via a ‘regular’ BB-assignment.
Maybe you can ask the students to hand in the same assignment in TurnItIn as well as in a ‘regular’ BB-assignment, then you have the originality-check in TurnItIn and the group-grade-feature in BB. But you will need to trust them that they hand in the same paper in both assignments then.