Disabling comments on cards
You can disable comments via the board's "Settings" in the board menu on the right side of your board. Click "More", then "Settings", then select "Commenting Permissions" and choose "Disabled". Only board admins can disable comments.
Why can't I find this setting on my board?
Commenting is disabled on Template boards, and you will not see the 'Commenting Permissions' option in your board menu until the board has been converted into a normal board.