How to hide trackbacks on wp-admin/edit-comments.php

While this is not impossible, this is very likely to have ton of edge cases and backfire in some. In a nutshell comments are retrieved with comment query, which can be adjusted with something like this (if in admin and comment type not specified then only fetch normal comments):

add_action( 'pre_get_comments', 'exclude_pings' );

function exclude_pings( $comment_query ) {

    if( ! is_admin() )
        return;

    if ( empty( $comment_query->query_vars['type'] ) )
        $comment_query->query_vars['type'] = 'comment';
}

However the problem is “any comment query in admin” is too broad and there isn’t much it can be narrowed down by.

Overall I would not recommend to mess with this.

PS excluding by author is not supported by native arguments and would be even more tricky with need to filter SQL.