I had FUE hair transplant surgery 8 weeks ago. I just tanned not knowing it wasn't OK. Did I damage the transplanted hair?

Tanning should not harm your transplanted hair but it may discolor the wound or scalp or affect the healing process.

At 8 weeks post procedure sun exposure will not effect graft growth.However,you should be careful because too much sun can cause some skin pigment changes in the areas that were treated.

At the 8 weeks mark you are in the safe zone but you should be cautious as you may get discoloration from sun exposure in the affected areas. Try using a sun protectant in spray form or wearing a hat next time.

At 8 weeks it isn't as bad as it would be if it was only 1 week. But it is always important to protect yourself from the harmful UV rays from the sun so a hat or sunscreen is always a good bet. 

exposure to UV light negatively impacts the healing process of grafts in the recipient area and will cause them to get a sun burn on each of them