Hey! Certified equine body worker here! Please don't let them do this! I've been a practicing equine body worker for a few years now and I've also been to a fair few equine dissections. The hyoid bone is extremely delicate, thin and easy to break. Doing manual adjustments of the hyoid bone can cause injury. I would 110% never let anyone do one on my horses, especially if there are no issues :)
the hyoid bone is so delicate that during the dissections it's is very hard to get out of the horse without breaking it.
Something as simple as pulling the tongue (which is something a lot of people do to 'release the hyoid,' but why would someone want to release a bone? Bones are meant to be not released at!) Anyway, something like tongue pulling can snap it and then your horse will be in pain and definitely not going well under saddle.
If they think your horse has a restriction in that area, there are other therapies that can help to release tension or restrictions in the tongue and throat area that dont require manual effort, these types of therapies are light touch like Bowen Therapy, Craniosacral therapy, Masterson Method. These I would be comfortable with a trained and experienced practitioner working on my horse to release tension in that area, but even with these methods, messing with the area that the hyoid bone sits in can affect a horses balance :)