Karen,
Provided the family memory is absolutely clear (and there is of course every reason to assume that it is) it seems to me that there are two possibilities:
1. There was a G. Tibetts who was in the Birmingham Home Guard and died on 26th December 1940. There was also a George Tibbitts who was in the Birmingham Home Guard and died on 26 December 1941. Therefore, two different people.
2. The record for George Tibbitts is incorrect - name spelling and date of death which should be 26 December 1941. The CWGC record is incorrect and his CWGC headstone is also wrong.
I think that before you can do anything about 2. above you really need to unravel the mystery suggested in 1. Is the G. Tibetts record right or wrong? If it is right, there were two men, both dying on the same day 12 months apart, both Home Guard, both Post Office. Not impossible but a heck of a coincidence! If it is wrong, that would be equally surprising as I think I remember seeing somewhere some separate confirmation of it.
I wonder if one of the Forum family history experts could have a look at this and perhaps resolve the mystery. (It would also be useful to know where your grandfather was living at the time of his death).
Chris