In the olden days you might have chosen that moment to hurl the contents of your bedpan out into the street!
Seriously though, is the grass part of the strata common property or public land? If it is common property, the owners corp might be able to put up a low fence to delineate it as private. It could be as little as 30cm high and the sort of garden bed border edging that just pushes into the soil and costs little. Your dog walker would have to be bold to lift the dog over.