You might try an oxygen cleaner.

If that doesn't work, I've seen professional carpet cleaners work what look like miracles.

If that doesn't work, if the carpet is too new to replace, you can try having it dyed a little darker color.

If you do have to replace it, be sure to replace the pad, too.

I wish you the best.

nothing works better than Nature's Miracle for pet stains!!!

was the vet curious about the high bilirubin levels? Seems like an unusual finding that should be researched. Often high bilirubin levels are associated with certain kinds of liver disease, or hemolytic anemias... if no blood test was done on your pet, I would sure recommend it.