Remove the 'Delete' option from the Payment List Quick Action
<?php
/**
* Plugin Name: Easy Digital Downloads - Alter Payment List Quick Actions
* Description: Remove the 'Delete' option from the Payment List Quick Action
* Author: Chris Klosowski
* Author URI: https://easydigitaldownloads.com
* Version: 1.0
*/

/* Remove the 'Delete' option from the Payment List Quick Action
 * This can require a fine tuning of the user roles, typically handeled in a plugin
 * Example: http://wordpress.org/plugins/user-role-editor/
 *
 * Source of snippet: https://easydigitaldownloads.com/support/topic/custom-payment-history-view-per-user-role/
 */

function ck_edd_remove_payment_delete_action( $row_actions, $payment ) {
    if ( !current_user_can( 'delete_shop_payment' ) )
        unset( $row_actions['delete'] );

    return $row_actions;
}
add_filter( 'edd_payment_row_actions', 'ck_edd_remove_payment_delete_action', 10, 2 );
To implement this snippet on your site, create a brand new, empty WordPress plugin and paste the above code inside.