Team members, by default, have access to view any schedule on projects they have permission to access. This includes: viewing the dates, task durations, predecessors, assignees, percentage complete, as well as viewing any files and notes.
Users with admin access can control and limit non-admin users' ability to edit the project Schedules.
To do so, go to Contacts > Team Members and click Edit from the ellipse menu next to the desired team member user.
If you check the Can also mark tasks complete permission under Schedule, the team member will be able to mark off tasks as they are completed from the Field Update View and Mobile App, but not make any other adjustments to the schedule task.
If you check the Edit permission under Schedule, the team member will be able to edit the schedule task. This includes: changing dates, task duration, predecessors, assignees, percentage complete, as well as adding and removing files and notes.