Remove the ability to import previous imported file
you can simplely remove it by using hook_form_alter 

don't forget replace  form_id and yourmodulename with yours  in following code

function yourmodulename_form_alter(&amp;$form,$form_state,$form_id){
    if($form_id=='feeds_import_form' ){
    unset($form['feeds']["FeedsFileFetcher"]['upload']['#file_info']);
}
}


update
in this section we prevent user to resubmit the old file,this mean if user push import button without browsed new file we prevent him to remport

function mymodule_form_alter(&amp;$form,$form_state,$form_id){
    if($form_id=='feeds_import_form' ){
      $form['#validate'][] = 'mymodule_prevent_import_validate';    
}
}

function mymodule_prevent_import_validate($form,$form_state){
    if(!isset($form_state['values']['feeds']["FeedsFileFetcher"]['file'])){
            form_set_error('upload', t('Not new file uploaded'));
            return false;
    }
}