To remotely control a user's Mac, access needs to be granted from the client's side - the permissions dialog can be opened by clicking on Help --> Check system access.
In order to remote control a Mac using TeamViewer, permission needs to be granted for:

Screen Recording
Full Disk Access
Once there click Request Access for each one, then a prompt will appear:

In the window that follows, click the padlock in the bottom left, sign in with an admin account and then tick the Teamviewer button; once done, click the padlock again to save changes, the close the window.
Repeat for each one.

Once these have all been granted, we will have access to the Mac in the following ways:

  • Screen Recording - Enabling this allows us to see the user's screen while in Remote Control
  • Accessibility - Enabling this allows us remotely control the mouse and keyboard
  • Full Disk Access - Enabling this allows us to access files and folders on the Mac in case we need to do a File Transfer