The seeds are incredibly small, and for me come up in the most surprising places. They seem to like cleared areas like the cracks in my pavers and along the edges of the beds or in new beds or pathways with no completion. I'd save the seeds and sprinkle on top of your compost. I think your seed germination will be better.
here is one that came up in the middle of the mossy brick barbeque area I am saving for seeds to scatter in my woodland area.