A few drops or a little splatter of blood can be removed by applying neutral spotter like Avenge and flushing with cool or warm water. Some drug store 3% hydrogen peroxide if needed as a next step.
If the fibers are saturated with blood, it needs at least a submersion washing and maybe to be tossed out. The deep, dense pile of wool rugs can made it difficult to remove 100% and any remaining blood is potentially hazardous.
Wear your gloves and goggles. Don't expose yourself to liability by leaving the customer with something that may not be 100% sanitary.