Very carefully with a seam popper remove the old, then tweezer out all the thread.
With a really sharp pair of scissors, remove any fuzzies from the interior, and then do them by hand. Simple process.
Make sure you use matching thread. Contrasting thread makes them visible, but period garments reflect that just like today matching thread was used when available. Most contrasting thread started out matching, and faded over 150 years.
Ms Lawson can shed light on thread dyes.
Oak Park # 864 F&AM