Thanks Tim and you must, must pull weeds as seedlings if there is a membrane below, not to have that problem.
I never leave a membrane like that below bark as yes, you need now to scrape off the compost (onto beds), then I would remove the membrane and if you want, add new shavings/chips.
Where I have no wooden sides, my paths are mulched by blackbirds flicking compost off the beds as they search for worms (I would prefer not…) and it helps keep the path soil in good condition, then I pull the small number of new weeds.