Dear Vinit,
Thank you for putting the details clearly.
1. Never have any direct communication with a contract employee except with regard to something directly connected with work procedure or quality. The moment you issue a notice of misconduct, you are giving proof that he is your employee, working under your direct supervision and control. After that, if the worker asks for permanency and shows this as proof, the court is likely to give a judgment in favor of the employee and make her your direct and permanent employee.
So what you need to do is to send an email/letter/notice to the contractor, bringing the matter to his attention, and then ask him to take appropriate action. Privately, you can tell him what you want him to do, but any show-cause to be issued must be by him.
2. Regarding the reply by Mr. Babu, he has brought out an important point that a contract worker working for 7 years is likely to be made permanent because it violates the rule that permanent jobs should not be contracted out. But it makes no difference whether the contract is licensed or not.