This is knitted darning. Or Swiss darning. I inserted white thread as guidelines (I should have made them double, I should have read my own blog post about it) then made rows of knitting stitches with yarn on a darning needle.
Not too bad. All the burned ends are on the inside. I made sure to catch only whole loops with the white thread. I guess I could take it out now, the thread, because all the knitted stitches are interlocked.