PHP Fatal error: Call to undefined method i18n_object_wrapper::strings_remove()

Hey there
I have been upgrading a very old D7 site from v7.10 to v7.39 and I am constantly getting these errors:

On the site itself (see attachment)

and on the CLI through Drush:

PHP Fatal error:  Call to undefined method i18n_object_wrapper::strings_remove() in sites/all/modules/i18n/i18n_string/i18n_string.module on line 839
PHP Stack trace:
PHP   1. {main}() drush7/drush.php:0
PHP   2. drush_main() drush7/drush.php:11
PHP   3. Drush\Boot\BaseBoot->bootstrap_and_dispatch() drush7/drush.php:70
PHP   4. drush_bootstrap_to_phase() drush7/lib/Drush/Boot/BaseBoot.php:54
PHP   5. drush_bootstrap_max() drush7/includes/bootstrap.inc:384
PHP   6. drush_bootstrap() drush7/includes/bootstrap.inc:438
PHP   7. Drush\Boot\DrupalBoot7->bootstrap_drupal_full() drush7/includes/bootstrap.inc:285
PHP   8. drupal_bootstrap() drush7/lib/Drush/Boot/DrupalBoot7.php:70
PHP   9. _drupal_bootstrap_full() includes/bootstrap.inc:2262
PHP  10. menu_set_custom_theme() includes/common.inc:5243
PHP  11. menu_get_custom_theme() includes/menu.inc:1772
PHP  12. menu_get_item() includes/menu.inc:1757
PHP  13. menu_rebuild() includes/menu.inc:460
PHP  14. menu_rebuild() includes/menu.inc:2739
PHP  15. _menu_navigation_links_rebuild() includes/menu.inc:2749
PHP  16. menu_link_save() includes/menu.inc:2894
PHP  17. module_invoke_all() includes/menu.inc:3252
PHP  18. call_user_func_array() includes/module.inc:895
PHP  19. i18n_menu_menu_link_update() includes/module.inc:895
PHP  20. i18n_string_object_remove() sites/all/modules/i18n/i18n_menu/i18n_menu.module:259
Drush command terminated abnormally due to an unrecoverable error.                                 [error]
Error: Call to undefined method i18n_object_wrapper::strings_remove() in
sites/all/modules/i18n/i18n_string/i18n_string.module,
line 839

What is going on here?

This seems to be a major problem and is putting the Drupal Update to a complete halt.