So the Treaty of Guadalupe Hidalgo gave all this land to US Government - yes
and anyone on the land can be removed - No.
Parcels of that land were given out sold distributed etc. Some of that land is in private hands. The land in question has never been sold by the US government and still belongs to the US Government as part of what is now called the Lake Mead National Recreation Area.
So the Treaty of Guadalupe Hidalgo gave all this land to US Government - yes
WRONG
Thanks for the additional information. The news reports are not clear about the grazing land which this ranch has used since 1870.