My immediate vote is for a pressure washer. They are relatively cheap these days. Lacking that, a simple high pressure hose nozzle and a good stiff brush will do well too. Various oxidizing bleaches will also work, all of which will last for only a limited time.
To stop it from returning is difficult, since any moist, shady spot under a tree or bush is likely to grow moss and algae of this sort.
One idea is to remove the overhanging growth from the planters. Trim them back. This will help the brick pavers to dry out, and will reduce the tendency for unwanted growth.
Another idea is to get creative, and buy some zinc strips. Copper flashing might work too, but they sell zinc strips specifically for roofing applications, where moss and algae tends to grow on roofs. The elemental zinc leaches out (very slowly) when it rains, which in turn inhibits growth of the algae where it leaches out. So you could afix these strips to the bottom edges of your planter. Make it decorative and it should help, although I cannot assure it will work perfectly. At least this will inhibit the moss.
Another idea is to buy/make a few copper pots or planters. Place them decoratively right on top of the problem spots. As the copper leaches out from weathering over the years, it too will inhibit growth on the walkway, you not be a problem for larger plants in the area. If you cannot find a pot you like, you can make a planter from wood, but then wrap copper flashing around it, nailing it in place.
Be creative if you wish to inhibit the growth.
The bleach mix will be dilute enough that it will not be of harm. I've used it myself at least a few times to kill off algae that has accumulated.
You can also use things like Oxy-Boost and Stain Solver, a bleach substitute which I believe contains some hydrogen peroxide. It will also work against light moss and algae, yet perhaps be less harmful to plant life underneath.
More importantly is to fix the source of the moss. Roofs that gather moss tend to be too shaded, under big trees that stop it from drying out. You may need to open things up, just by a bit, but enough to let it dry out. Yes, those trees are a natural source of air conditioning, but trees tend to grow. So trim off branches that overhang the roof. Cut a few others out to let the sun in.
For roofs that have only a bit of green, you may find it is sufficient to add zinc strips along the top. The zinc leaches out, keeping the roof clean of moss accumulation. There are also shingles with a moss inhibiting additive that prevents moss from growing. Copper strips should also work, and copper flashing is easily available. I've even read that you can glue (use silicone) copper pennies just under the edge of the top row of shingles. They are mainly zinc anyway.
If the moss had accumulated heavily, the problem is your roof likely needs repair, as it will have been too wet for too long. The shingles will need to be stripped off and replaced, but probably the roof decking will be soft and need some repair too. This can best be judged by a professional who will inspect the roof carefully.
Best Answer
We use a bare galvanized wire fastened to the ridge of the roof.
If you’ve ever noticed a “clean” area under (downside of slope) chimney flashing or metal roof vents, you’ll understand the use of galvanized metal to keep the roof “clean”. (I’m sure some chemist could explain why the galvanized coating keeps the asphalt shingles “moss-free”. )