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In the classical way we think of the body, there won't be a lot of genetic changes if the ovaries, uterus (or the testes for that matter) are removed from the body.
The main effect would be that the sex hormones that are produced in these organs would no longer be present and this would have a profound effect. So the broad answer might be 'no genetic effects but large endocrine changes'. Endocrinology is the study of glands and their function in the body. Growing cysts, tumors as well as other effects seem like reasonable effects to see for such a drastic change in the body as removing the reproductive organs.
If I were hard pressed though probably this might end up with some small genetic effects compared to an individual who had never had the organs removed. Mutations happen frequently in many of our tissues and also they respond to the environment to methylate the genome and modify it in non-genetic ways ( known as epigenetic effects). This is purely conjecture but its also found that nearly everything has some effect on the cells.
hope this helps.