Hello Donald, thanks for your question. Applying herbicides to suckers can kill the whole tree, so as long as the neighbors no longer have their tree (ie: it has been completely removed permanently), then you could apply a herbicide without potentially damaging the mother plant. As this looks like it's coming up through your deck, spraying may not be an option as you don't want to damage your surroundings. You may like to consider trying 'Yates Zero Weedkiller Super Concentrate'. Click here for more info on this product: https://www.yates.com.au/product/weed-control/general-garden-weed-control/yates-1l-zero-weedkiller-super-concentrate/

Cutting the stems down as close to the ground as possible under your deck, and applying the solution immediately to exposed stems will yield the best result. You can make a very small amount solution up, using the rates on the back of the product and apply liberally.