@luna69,
I am a transplant recipient. I remember being asked during my initial interview/screening in 2009, whether I had any tatoos. (I do not) When I asked the reason for the question, I was told that if a tatoo was done at a reputable/licensed tatoo parlor that it should be fine. But if someone got a tatoo elsewhere, there was a risk because some amateur artists don't always use sterile technique. This could lead to transmission of viral diseases.

An important part of the pre transplant process is to treat or eliminate any potential risks. As others have already suggested, your transplant team is the best place to ask this question. With the popularity of tatoos, they must get this question quite often.
@luna69, I think that this is an excellent question. I hope that you will get an answer that will be satisfactory for you. If you are comfortable to share what you find out, I am interested to hear what they say about tatoos.