Wrap your self up in PPE, lift the carpet replace the pad, clean the back, dry it and reinstall it, clean the pile again with peroxide based cleaners and loads of 40 volume them leave a poultice on it to deal with any more wicking
Or you can try using a water claw to flush out the remaining blood.Most likely it will take a ton of flushing do leave a fan behind to dry the carpet.A poultice would be a good idea too but you'll have to let it dry before running the fan
Regardless of how you go about it, a few visits will be needed, so charge accordingly.
Make damn sure the person who bled out wasn't sick(aids)
Good luck!