remove anything bridging the DPC most urgently. It is usual to remove the render above the DPC as your second priority, so the bricks can dry out.
I personally would also remove the render below the DPC, but this part is "allowed" to be damp, and the bricks may have spalled due to frost, so they may look unsightly when bare. I don't know if a lime mortar render below DPC would be acceptable. I will see if I can find an example locally. I don't remember seeing one.
IME water will only rise about two courses of clean, bare brickwork, above ground level. But there might be plaster on the inside face, or a cavity filled with damp rubble, which will encorage water to move by capillarity.
What tool are you using?
A bolster and a club hammer are the simplest and cheapest tools. Wear substantial gloves and choose a bolster with a protective collar. You will hit your hand.
bolsters
you can get bolsters up to about 150mm wide. 75mm is a good start, because you can also use it for electrical backboxes later
It is absolutely ESSENTIAL to wear eye protection, and I strongly recommend ear protectors.
Club Hammers. If you are a bit weedy, get a lighter one.