They are pockets, unfortunately. I actually just skimmed a reddit thread and someone mentioned a tonsil stone vacuum! I checked Amazon, and they seem to have a plethora of specialized tools. The battery-operated vacuum mentioned, what is essentially a straw on a bulb syringe for a manual vacuum, and specialized tonsil stone picks. Just search up tonsil stone remover and you may find something that looks tolerable.

If it's a persistent problem or something painful, it may be worth it to see an ENT to see if you should have your tonsils removed or if they can offer a solution that works. Things like mouth breathing, post nasal drip, and not staying hydrated can worsen accumulation of stones, so treating any of those conditions could also alleviate some of it.