Buckingham Palace did not announce the death of Miss Fane, 89, on June 7 last year, in an NHS facility for "adults with learning disabilities" in Redhill, Surrey.
It was registered by a "client assets manager" from an NHS Trust, and she was buried in council-run Redstone Cemetery, with a basic headstone.
Katherine was listed as dead in Burke's Peerage in 1961.
They went to Ketwin House, a care home for the mentally disabled, also in Surrey.
Ketwin House was closed last year after allegations that male staff had been washing female residents and that patients had been found wandering on country roads.
That is quite unfair on her and other members of the family.
I can say she was properly looked after until the day she died."The decision to move her from Ketwin House did not contribute to her death.
She had been very poorly for a long time," she added.