If you have no poaching agreement, then you can write to the vendor to revoke the offer letter/employment of the employee. If you are still willing to provide the relieving letter, then issue the standard letter given to every employee who leaves. However, please note that encouraging this practice may result in increased attrition in the future, with more people moving to the vendor's company.
Note: If any employee has resigned and joined the vendor company, please instruct the vendor that the employee (who previously worked in your company) should not be assigned to your company for any transactions. This precaution is necessary as the employee is familiar with the processes and procedures, and there is a risk of malpractices.
Prevention is Better Than Cure