Brick acid is the answer but be careful if you have not used before. You can buy this with varying strengths of hydrochloric acid. If you really must dilute then always add the acid to the water, never ever the other way around.
Be sure to soak the area thoroughly prior to applying the acid. If areas of staining are small then apply using a paintbrush, this is much safer in every way, to you and the bricks!
You will see the acid fizz up on the excess mortar as soon as applied. Leave on no more than 5 minutes, usually less on a small test patch. Rinse of with low pressure and your fan nozzle.
If larger areas and you have not done before then I would steer clear.
If you do go ahead be sure to use the following PPE: -
Chem res suit with hood.
Chem res goggles
Chem res gauntlets
Chem res respirator
Chem res wellingtons
Have a supply of water close by and someone briefed on what to do in case of an accident.
Most customers will insisit on a method statement, risk assessment and COSHH.
Check with your insurance that you are covered. Our policy more than doubled when we included the cleaning of building exteriors.