Dear "Arballen",
I don't really know what the common practice is in such cases. But you might want to ask yourself if you would have the same concern over organs or tissues that were removed from you because of disease (e.g. your appendix, a diseased kidney, gall bladder, etc.) Would you be concerned about what they did with the removed part? I'm only asking because there is so much emotion and personal concern involved when we donate a kidney to someone that we might tend to look upon that organ in a different way than other body parts we may have lost. Perhaps your concern over the recipient's health and your sadness over the deterioration might influence the way you think of the donated kidney? I don't know if this thought is helpful or not, but I pass it along anyway.
The gift you gave was (and is) a precious one, and that value and love cannot be lost. If you generously gave someone a used care because the person really needed one to get to work each day you would be happy if it was well used for some years, and not be too sad when it finally broke down beyond repair and had to be scrapped. Of course a donated part of our own body is NOT like a used car, but the love with which we give is the most important part.
Fr. Pat