Dear Sir,
In your case the GST charged by hospital is proper. Now the issue will be you can't avail the ITC of the same due notification no.13/2018 C.T.(R) dated 26th July 2018 clarifying the notification no. 46/2017 C.T(R) dated 14th November 2017.
Only way to avail exemption from GST levy by Hospital on this transaction is through Pure Agency Concept.
Pure Agent is the person enters into a contractual agreement with the recipient of supply to act as his pure agent to incur expenditure or costs in the course of supply of goods or services or both; neither intends to hold nor holds any title to the goods or services or both so procured or supplied as pure agent of the recipient of supply; does not use for his own interest such goods or services so procured and receives only the actual amount incurred to procure such goods or services in addition to the amount received for supply he provides on his own account.
Further, in order to fall under Pure Agency following conditions has to be satisfied:-
(i) the supplier acts as a pure agent of the recipient of the supply, when he makes the payment to the third party on authorisation by such recipient;
(ii) the payment made by the pure agent on behalf of the recipient of supply has been separately indicated in the invoice issued by the pure agent to the recipient of service; and
(iii) the supplies procured by the pure agent from the third party as a pure agent of the recipient of supply are in addition to the services he supplies on his own account.
Kindly analyse your situation whether the Hospital can act as a Pure Agent, If not so whatever the Hospital is charging is proper as already explained by Mr. Kasthur Sethi sir.