This is from modern day India describing about a woman who discarded veil in Rajasthan
Born into a family of daily wagers, it never really seemed likely that Murli Meena would achieve this desire. Although she was a natural leader, there simply were no opportunities for her to distinguish herself. Her fortunes, however, changed when she got married to someone who lived in the neighbouring village of Dehlala and decided to discard the 'ghunghat' (veil traditionally required for all married women). Looking back, Murli says she wanted to "live as freely as the daughters and daughters-in-law of the Brahmin and Jain communities in my neighbourhood". Says she, "During the 'pheras' (Hindu marriage ritual) when my mother pulled my 'pallu' (free end of the sari covering the head up to the waist) down, I pulled it back with equal force - and this happened quite a few times!"
While initially no one liked her "bold move" - for quite some time she had to bear the criticism and nasty comments of her family and friends - slowly everyone reconciled to the change
Impact of Islam?
Well Islam was born in 613 AD. Now there is an ancient sanskrit work which is a biography of Buddha @Tshering 22 . This work was already translated in Chinese in 308 AD and is known as Lalitvistara meaning Play in Full ( vistara = full, lalit= play). When Buddha was married to Gopa( Yasodhara) this is what she faced
"However, no matter who the ÅšÄkya girl GopÄ encountered, whether it
was her mother-in-law, her father-in-law, or any other member of the inner quarters, she did not cover her face. So people criticized her and spoke badly of her, saying, "A new wife is supposed to be covered" '
Do you know what she said?
"Those who control their bodies thus control all physical faults;
Those who control their speech never confuse their words;
Those with guarded senses are mentally composed and serene.
What good is it to cover the face of such beings?
"Furthermore the great sages, those who know the thoughts of others,
And the assemblies of gods all know my thoughts.
They know my discipline, qualities, restraint, and carefulness;
So why should I veil my face?"
So no that woman in Rajasthan is not wearing veil due to islam, she is wearing it because Buddha's wife was also asked to do same. No islam here.