Relevant clause is Article 41 which states,
1. Consular officers shall not be liable to arrest or detention pending trial, except in the case of a grave crime and pursuant to a decision by the competent judicial authority. (Grave crime is usually defined as Murder, Rape, Robbery etc. )
2. Except in the case specified in paragraph 1 of this Article, consular officers shall not be committed to prison or liable to any other form of restriction in their personal freedom save in execution of a judicial decision of final effect.
3. If criminal proceedings are instituted against a consular officer, he must appear before the competent authorities. Nevertheless, the proceedings shall be conducted with the respect due to him by reason of his official position and, except in the case specified in paragraph 1 of this Article, in a manner which will hamper the exercise of consular functions as little as possible.
Article 72 does discuss customarily favored treatment beyond the limits of the Convention. This could be what infuriates Indian officials so much.
privilege that consider exists under Article 72.