No, there is no requirement to join any insurance company for the Gratuity Scheme. However, if your employer wants to take tax benefits on provision, then you need to enroll with an insurance company.
Only LIC has a limitation to enroll new clients up to 31-08-2013 as per the notification by IRDA on 16-08-2013. For new clients after that date, Gratuity schemes will be closed for enrollment. Please confirm the same from your side.
Thank you,
Regards,
Ashish