OK .. go into the Admin Control Panel / Groups / Permissions (for the General group) / Attachments .... highlight all the forums you do NOT want the general group to be able to upload attachments in. This may seem a bit counter-intuitive, since the highlighted forums are not allowed to have uploaded attachments for this group, but when you select anything other than "allow all" it becomes a restriction. Then click on the "save" button.
Now the "attach" button will not show for members of the General group in those selected forums.
(and remember to reset your max number of attachments in the control panel back to what it should be for other groups that are allowed to post attachments ... default is 3)