When making a submission to an assignment in Canvas, students have the opportunity to provide a comment alongside the submission. When feedback is left against a submission and this is released to students ('posted'), again students can add a comment to reply to the feedback, that appears in SpeedGrader.

This appears to be a core feature of Canvas/SpeedGrader and is not something that can be disabled. This features regardless of the submission type, for example if Turnitin is used there is still a route for feedback and comments to be left via SpeedGrader.

The approach set out so far for staff has been:

Let students know what methods they should use to communicate with their lecturers (via email etc.) . If you do not wish students to comment on feedback then let them know not to use this feature.
Let students know the degree to which there can be dialogue about grades/feedback: is there a limit to the amount of follow-up each student can have? Again is there an 'approved' route for this such as office hours?
If student comments are welcomed against an assignment, or if students are leaving comments in the absence of instruction, staff can quickly see any comments through the Inbox.
If students are communicating inappropriately, the University has policy to govern IT system usage: https://www.liverpool.ac.uk/media/livacuk/computingservices/regulations/IT_Acceptable_Use_Policy.pdf#page=8

There is some good discussion here around ways to frame this with students: https://community.canvaslms.com/t5/Canvas-Question-Forum/Turning-off-student-comments-in-Speedgrader/td-p/119469