Export is obviously an important feature, and capabilities exist to control access to this feature.

The export button appears in the top left of Landing Pages.  Users with export capabilities will see this:

Those users without the capability will see this - no export button:

To control access you need to understand and make use of User Groups.  The Knowledge Base documentation and this forum article explain the background - How do I add/remove users to/from a user group? How can I add/remove capabilities?.

If you do not want a User to export you need to check their capabilities tab and which User Groups they belong to.  If they do not belong to a User Group that has export permissions they will not be able to export.  If they do belong to a User Group that has export permissions they will be able to export.

If you want to revoke a User's export capabilities you'll need to make sure that they do not belong to any User Group with export permissions.

Here's an example of a User that cannot export.  Note that they belong to two User Groups, and have 6 capabilities, but neither of those User Groups grants them export capabilities (Click to enlarge):

If you wish to grant export capabilities you need to ensure the Users are members of User Groups with the relevant capabilities (Click to enlarge):