There are a number of checklist permissions:
mod/checklist:edit - can change the checklist
mod/checklist:emailoncomplete - get notified when a user completes a checklist (if enabled in settings)
mod/checklist:preview - view a checklist without updating it (only checked if they don't have 'updateown')
mod/checklist:updatelocked - update check marks even if they are considered 'locked' (if enabled in settings)
mod/checklist:updateother - edit the teacher mark on another user's checklist
mod/checklist:updateown - tick off items on your own checklist
mod/checklist:viewmenteereports - only view reports of those you are a mentor for (rarely used)
mod/checklist:viewreports - access the report view
Choose the combination of capabilities you want from this list.
(if you don't give teachers the 'edit' capability, then they won't be able to edit the list)