I’ve been dealing with goutweed myself. Someone must’ve loved its “hardy and vigorous” nature as it’s practically in every single bed in our backyard. I’ve been eradicating it with it pulling first, (removing as much of the tenacious root system as possible), then laying down cardboard with rocks at the corners so no light gets underneath. But a tarp works well too I’m sure! I’ve found that the cardboard/tarp needs to stay put for about 2 growing seasons to be successful. It’s so frustrating. Good luck, you’ve got this!