How is the holy grail war from Fate/ Stay night kept a secret?
From the author Kinoko Nasu himself:

The Holy Grail War is unknown to the general population, but to what extent is it hidden from normal people? Are the Church people (supervisors) manipulating the media and police (or even the governmental level) to cover it up?
A: The Church manipulates information, while the Magic Association handles the media. Also, the Association has the Einzbern cover the cost of any collateral damage.

Fate/complete material III: World material - FAQ with Nasu: Holy Grail War, p.131
Eyewitnesses can be dealt with by manipulating their memories.