An annoying puzzle

You know how you get little niggles and questions that ought to be simple to sort out, and they aren't ?   And they get bigger and bigger in your mind, and you can't leave it alone  .... stupid, I know !

Well I've been trying to find the answer to something ALL day (it has been raining heavily most of the day, so I had a good excuse !)    Maybe one of my ex-pat friends who read this, or anyone .... can tell me the answer.

Look at this map of a bit of N. W. Kenya:-

If you have a decent modern atlas, you will see this little bit of desert and dry bush (which I've indicated) is supposedly 'under Kenyan administration'.    Why ?

Does it belong to Kenya, or South Sudan  to the west, or Ethiopia to the east, all of which it shares boundaries with, or perhaps even Uganda to the south-west ?   

I have googled; looked in my massive 1970 Atlas of Kenya published by Survey of Kenya; checked in a modern atlas .... all to no avail.   

The ground to the west of it is part of S. Sudan, a district called Namorunyang .... see https://en.wikipedia.org/wiki/Namorunyang_State.   But it doesn't seem to include this little snippet of land .... 

Maybe I need to wash the dishes and have an early night !!!