I am three weeks post FUE surgery with 1700 grafts. When would it be safe to return training jiu jitsu?

After 3 weeks from an FUE hair transplant procedure, you should have nothing to worry about as far as returning to your regular physical activities, including Jiu Jitsu. The donor sites are all healed, and the recipient areas are also safely healed. Just make sure you wash your hair very well after training, in order to clean it well.

In general most doctors would suggest 3 weeks after a hair transplant surgery (FUE or FUT) before resuming heavy exercise or contact sports (which include combat sports and grappling).  Most importantly, ASK YOUR OWN DOCTOR as they have have specific issues with your specific surgery and circumstance.  

There's usually no issues with intense exercise at 3 weeks provided everything has healed nicely. It's always a good idea to run the question by your surgeon in case there are specific details about your surgery and post op course that might actually benefit from a bit longer rest. But 3 weeks is generally okay.