Aim at the Memorial and Kowalski will become angry; shooting at it will make him furious.
Keep being disrespectful or apologize (Speech 30).
If the Courier insults him and his brother, the Courier receives negative Karma and makes Kowalski hostile. Killing him this way doesn't make other people hostile.
If the Courier doesn't apologize, they receive NCR infamy. If they shoot at the memorial, this makes all people hostile, including Kowalski.
Whether the Courier has completed the quest or not, Kowalski will disappear after a few days.
The stone can be defaced with unarmed weapons, or indeed no weapon, by punching the stone.
Defacing the stone when hidden has no effect on one's standing with Kowalski or the NCR.
Taking a picture of the stone with the Codac R9000 will cause Kowalski to react as if the Courier shot it. This is because the R9000 is coded as a ranged weapon, and fires invisible projectiles that normally don't anger NPCs.
Kowalski may state that the Courier defaces the monument when they did not. The Courier will have to pass the Speech check to avoid NCR infamy and once passed, Kowalski will no longer speak to them.[verified]