The three-member panel, set up by the club today, will include lawyer Renu Sehgal and journalist Sunayana Arora Singh, the CEO and founder of an NGO, Organ India.
"Since there are conflicting versions of the incident, it is deemed appropriate to institute an inquiry by independent persons who are not members of the club," the club said in a statement.
Lyngdoh said the manager informed her that the outfit she wore was not allowed in the club.
The club, an elite golfing establishment situated in acres of rolling greens, added that Shailja Laxman, its HR manager, will provide administrative assistance to the three- member committee.
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"The club shall take further action in this regard after receiving the report of the inquiry committee," it said.
The Union urban development ministry also sought a report from the club on the issue.
The Delhi Golf Club said yesterday it had apologised to the member who had invited Lyngdoh and her employer to lunch but added that Lyngdoh had not been asked to leave the club.
Mudgal, retired Chief Justice of the Punjab and Haryana High Court, had earlier headed a committee which was directed by the Supreme Court to conduct a probe into allegations of corruption in the Indian Premier League.