Well, it’s a non-free plugin so I don’t know anything about the implementation and there does not appear to be a published API documentation, so you would have to ask Thrive Themes whether there are any hooks to customize the comment form. Avatar Privacy includes such an integration for wpDiscuz which similarly completely replaces the standard WordPress commenting system, but that’s available here in the plugin repository.
If you want to do it yourself, you would have to check what they do for (Gr)avatar handling and replace that with the standard get_avatar() function. You should call Avatar_Privacy\gravatar_checkbox() somewhere in the comment form to output the “Allow Gravatar” checkbox and if necessary, add some code handle the form submission (if they don’t use the standard WordPress hooks). Additionally, to make these things work dynamically, you might also need some form of JavaScript integration.
Since this is about integration with a commercial plugin, your best bet is to contact their support, they should have all the information available. I’ll gladly answer any specific questions regarding integration.
