In case of Hotel Reservation, the place of supply is location of Hotel, so they charge CGST and SGST. Now, if a person located in Delhi stays in a Hotel in Mumbai (business purpose), can he claim ITC of that stay? Secondly, In travel industry, Travel agents are bypassing place of supply rule, by adding a travel agent of Mumbai state in the transaction who first claims the ITC and then issued IGST invoice to customer in Delhi. Is this transaction legitimate from GST point of view?

No, in my opinion, travel agent who is availing Input Tax Credit of accommodation services (Hotel room) cannot change the nature of supply of accommodation to tour operator services and charge IGST on such services in case they charge for such accommodation services from person in other state. The definition of tour operator does not cover individual services of Hotel accommodation but it is defined as "Tour operator" means any person engaged in the business of planning, scheduling, organizing, arranging tours (which may include arrangements for accommodation, sightseeing or other similar services) by any mode of transport, and includes any person engaged in the business of operating tours. Thus, the presence of a tour is important.    Similarly, in case of reservation services, the principal supply of accommodation is not provided by supplier but merely its arrangement.