While neither Turnitin, nor Handin have a specific 'no grade' option, both can be used for formative assignments in which the focus is on providing detailed feedback to students rather than grades.
If you need a similarity score (plagiarism checker) for your ungraded, formative assignment, you will need to use Turnitin.
Turnitin does not have a 'no grade' option when creating an assignment. Turnitin grades are always numerical.
However, it is possible to simply not enter grades and to use Turnitin's feedback features to provide detailed feedback on student submissions only.
At the point that grades are released to students (this is a pre-determined date defined when creating the assignment), if there is feedback but no grade, this is exactly what will be released to the student. The grade field will simply be blank.
When using Turnitin for formative assignments, it can be a good idea to activate the 'Do not store the submitted papers' setting. You can find this in 'Optional settings' in the assignment in Turnitin.
If you're using Handin, have a look here - Handin: Create an Ungraded and/or Feedback-Focused Formative Assignment