Is laser tattoo removal safe for people who had kidney transplant?

It should be fine to have laser tattoo removal, but you should check with your Doctor. Tattoos should be removed with q switched or pico lasers. Using a PFD patch in tandem with a laser will get you more removal quickly as compared to tattoo removal without it. It will take a series of treatments, but it's difficult to determine how many treatments you'll need. I recommend getting a formal evaluation with a laser tattoo removal expert. 
Best, Dr. Emer

The ink is not excreted through the kidneys so the procedure is safe for kidney transplant patients. Your healing time will be impaired due to the immunosuppressive drugs and the clearance might not be as good as someone not on these drugs. The process of removal requires the immune system so if it is dampened, you might require more treatments. In the case you go burned, the healing would also be delayed. The Pico lasers are safer because they generate less heat and are more targeted than the nanosecond lasers.

This is an excellent and thought-provoking question. 
You are correct that we rely on certain cellular immune functions for laser tattoo removal. While the system is complex and is composed of many discrete parts, there are many communications among these parts, some of which have been suppressed for your kidney transplant.
Therefore I’d recommend taking an extremely cautious stance regarding tattoo removal. With a risk as significant as graft rejection, I would recommend avoiding any elective procedure that poses any threat of infection or other stresses to your cellular immunity.
If you are determined to remove a tattoo despite this, be sure to put this question to your transplant team and get their full blessing before proceeding. 
And, as always, I recommend having no less than a physician doing your laser procedures.
Best of luck to you!