Depending on how bad the mortar stains are, I suggest trying standard cleaning methods first with water and detergent in combination with a scrub brush.
If the stains are persistent, I recommend using Chemtech 1L Brick Tile And Paver Cleaner. A lot of trades people use this product to clean mortar and concrete slurry. Please note that this is a concentrate and must be diluted before use.
Please remember to wear personal protection such as gloves, goggles and a mask when using the cleaning product. Please make sure to follow all the safety precautions printed at the back of the bottle.
A more aggressive approach is wet grinding with a strip disc. However, wet grinding has its own set of after-effects. If the brick face has already aged, it is possible that any area you polish with the grinder will now look fresh and brand new. The area you did not polish will have its old finish. It would mean, you would need to grind the whole wall to give it a uniform fresh finish.
I would always suggest testing a small inconspicuous area first and see if it removes the mortar and whether it changes the appearance of the brickwork. - EricL
