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Was there blood in the abdomen at the time of diagnosis?
When the spleen is removed, there is often some bleeding into the abdomen. This blood will get broken down by the body and need to be excreted. When broken down red cells are excreted, it'll turn the urine an orange/ red color. It also makes the bilirubin increase, as hemoglobin in red cells is the same type of compound as bilirubin.
I think it's that breaking down and excreting of red cells that is causing the high bilirubin in the urine. This should be a transient finding and it should resolve over the next 5-7 days on it's own.
I hope this helps, let me know if you have any other questions.