I think any armor and weapons of the dead should go to their heirs only. Once you give some equipment to a NPC to wear, it's his, so it's doubly inappropriate to strip it back off his corpse.
Only if he has no natural heirs and he wrote a will making you the sole heir, you could take it off, but you should still be viewed as a graverobber in a polite company.
That is true, I agree that it should go back to the family members. But no one in the clan, besides yourself, has any heirs, and the non-family companions do not have any family lineage. I am not suggesting taking the gear from other fallen lords outside of your own clan, unless its your fallen enemy. I believe the gear should fall into their own clan leaders inventory.
Historically fallen nobles loot was given to the family. Nobles who died in battle were not just left in there armor and buried on the spot. There was a ceremony. The three main ways medieval soldiers obtain armor was through inheritance, gear from dead enemies on the battle field, and renting armor from lords. Because owning and maintaining gear is expensive and heavy. It might seem inappropriate, but its the medieval era not the present time.
With this in mind, its more likely that the gear you gave to the companion is being rented out rather than being given to keep forever. Which is why you can take and remove the gear at anytime of there existence. Plus no one is ever buried, cremated, or laid to rest with the clothes they died wearing in modern times.
Everything you currently suggested like wills and inheritance is sadly to complicated right now. I am more focused on a simple fix to help the players game experience.