During a walkway pour some concrete residue smeared on the existing landing pad and entrance (both old concrete) causing a dirty appearance.
Is there a way of cleaning a smear of concrete from old concrete slab underneath?
Muriatic acid is the usual way of cleaning up cement-based products. It may act more readily on the newer concrete, but use caution and be prepared to rinse thoroughly if the outcome isn't ideal.
If the concrete is very new, try a water rinse along with a wire brush and some elbow grease.
A pressure/power washer will help the old concrete look new. Typically, a 3000 PSI or greater power washer is used on concrete. I have one not quite that powerful, but I used a narrow angle on the sprayer and my driveway came out looking many years newer as well as knocked off loose concrete which I think would help you resolve this problem.
Best method is prevention. Depending on how the concrete is poured and how much water it has its splash can travel quite far. Cover the neighboring regions, I would say as far as 4 feet away, with a tarp. Even though a thin layer of cement is not supposed to stick, it does sometimes and looks like paint splash. Protect other structures like windows, doors, etc.
Some remedies for removing it from concrete
1- Chisel the big pieces off. Wear eye protection.
2- Use a brick an an eraser, (There is also a commercial "concrete brick rub" you can get from hardware stores for 10-20 dollars. It is a hard stone with a handle).
3- Use a pressure washer (as mentioned by UnhandledExcepSean) , wear eye protection.
4- Use muriatic acid, (as mentioned by isherwood) being careful that its vapors are very toxic, be ready to rinse to prevent damage to base concrete or metal. It is not friendly to plants either. You can neutralize it with baking soda, soda ash and lime. Wear protective gloves and eye protection.