"My mother never asked for this provision, and I am sure its removal will at least save her from the embarrassment and discomfort she always felt over the unnecessary inconvenience they sometimes caused to others despite her requests not to do so," Mr Vadra said in a Facebook post.
He also accused sections of media of a "tirade" on the issue.
"There are more civilised ways of changing things than running a media tirade, in which a senior citizen is hounded and the media is informed even before the people concerned are regarding security arrangements for them."
"I reiterate...please don't take your fight with me, to my mother at least," he added.
The Delhi Police on Tuesday removed the security cover of Mr Vadra's mother, Maureen Vadra, a senior police official told IANS.