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Thakur said being the main financier of Olympic sports in the country, the government has every right to take call on matters of national representation.
The Delhi-based Manika had won an unprecedented four medals at the Games including two gold medals, a silver and bronze.
The Indian Olympic Association has offered to host, at New Delhi or Chandigarh, separate Commonwealth Championships for shooting and archery months before the actual Games begins in Birmingham.
The organisers said that more than 6,000 athletes and officials will be housed at the universities of Warwick and Birmingham and in hotel rooms at the National Exhibition Centre.
The IOA also approved the National Rifle Association of India's (NRAI) proposal to host a separate Commonwealth shooting championship before the main Games in Birmingham, hoping to make up for the sport's withdrawal from the roster of the 2022 edition.
The Indian Olympic Association has already threatened to boycott the Games over exclusion of the discipline which supplied 16 of their 66 medals, including seven golds, at last year's event at Gold Coast when they finished third in the medals table.
IOA chief Batra had said the level of competition at the CWG was not particularly high and that India should consider a pullout to improve its own standards.
The Indian Olympic Association has already threatened to boycott the 2022 edition in Birmingham due to the exclusion of shooting.
Shooting has been a high-yielding discipline for India with shooters accounting for 16 of the country's 66 medals, including seven golds, at last year's Gold Coast Games.
The women's T20 event is one of three new disciplines added to the next edition of the Games, alongside Beach Volleyball and Para Table Tennis.
Results 51-60