The theory that any tissue can remain is pretty much history, as far as I know, because any active thyroid tissue is capable of reacting to the antibodies, so even half, or a quarter, of a healthy thyroid can still end up making us hyper, over time, unless it’s managed with ATDs.
Having said that, nearly all the time, a TINY TINY percentage of thyroid tissue is left as is because the parathyroids are attached to it, which help regulate our levels of calcium. From what I hear, the parathyroids can actually be removed from the thyroid and "stuck" somewhere else and they will still function, but in most cases the tiny bits of thyroid they are originally attached to are left behind just to make sure. Those teeny tiny bits would not be capable of causing trouble, but the surgeon still can’t call it a "total" thyroidectomy if tissue remains. I think usually they call it "sub-total thyroidectomy."