not updates taxonomy_index on deletion

There's no way I can help you with the current description, I don't understand what the issue is, sorry.

I don't think there's a way for Backoffice to interfiere with that process.
Are you using a term reference field, or an entity reference field for your taxonomy?

it seems this is an Inline Entity Form issue.
and it happens for product reference fields with "delete_references" setting set to TRUE.

i don't know why as taxonomy_node_delete() & taxonomy_delete_node_index() do take place.
is there something the IEF controller that doesn't allow the db_delete from taxonomy_delete_node_index() to be executed?

i didn't test for other reference types.

Since Drupal 7 is now end-of-life I am closing some old issues for the 7.x branch of this module. If this issue is still relevant for the 3.x branch of the module, then feel free to reopen it.