I would take sewing yarn - the thin stuff for the machine. And catch all the top stitches with it. Then tie that off. If you stay to the inside of the tumbhole, it will - hopefully - not show. If the color is similar, it will be even easier.
Just be careful not to pull a tight ring into the thumb... then it would not fit or not be comfortable.
I guess you could secure the last knot with a drop of super glue, too. But I have only read about this, not done it, so take this advice as a hopeful thought, not spoken from experience.