should not be an issue unless removed due to cancer. Potential donors with a history of some types of cancer are excluded. Some donors have had previous surgeries to remove organs or tissue like tonsils, appendix, uterus (not related to cancer). It is also a good way to know how you reacted to anesthesia. During the initial contact the nurse should review past medical history. They usually look for things like high blood pressure, diabetes and cancer initially to determine eligibility to donate. There is a lot of information on this forum about the process so while waiting it is a good way to become educated.
Good luck on the transplant journey for you and your family.
Sherri