The British actress-model and Nayar, 42, were married last month in a lavish and traditional Hindu ceremony in Jodhpur. The event drew the ire of a Hindu religious activist, who filed a complaint saying it had mocked Hindu customs.
Meanwhile, tabloids in England and India carried reports that Nayar's father, Vinod Nayar, severed ties with his son after he was thrown out of the wedding on Hurley's urging.
When asked how this has affected the couple, Hurley told AP Television News that it has made her "incredibly grateful for the nice people" in her life.
"We're so lucky for the good things that we kind of turn a blind eye to the bad things," said Hurley, who called her family "fantastic."
The 41-year-old actress, who attended an event for the Breast Cancer Research Foundation in New York on Tuesday night, said she hasn't "settled down into real life yet."
"The whole wedding took forever. The wedding itself took eight days; planning it took considerably longer; recovering from it; I'm still not sure I have," she said.
Hurley and Nayar first wed in a private civil ceremony in a castle outside London.
The complaint about their Hindu wedding says Hurley wore revealing clothes and didn't remove her footwear while walking around the sacred fire at the ceremony.
The petition was filed under a section of the Indian Penal Code that makes it an offense to upset any religious feelings with "deliberate and malicious intention."
India's legal system is notoriously slow, and it could take months and even years before complaints come up for hearing.
Hurley appeared in "Austin Powers: International Man of Mystery" and "Bedazzled," and for several years was the international face of Estee Lauder cosmetics. She has a 4-year-old son, Damian.