No burrs that I can tell. Its not responding to a pherbicide. If it helps I think it is a speedwell. Spread by mulched bits fits, herbicide should have done it but I have so many grass types I have to go easy. There is everythng but zoysia out there.Can you get a closer pic please? Maybe next to a coin for size. Does it have sticker burrs?
Could you dig a plant, including the root, and take a photo of just it. Maybe on concrete or a sheet of paper, just a way to get a clear individual shot, how it branches and what the leaves look like. Any flowers or seed pods might help a lot.
I did that with a type of grass I have in the lawn and sent the photo to the Extension Agent. They IDed it as Dallisgrass, mainly by the flower. There is no selective herbicide that will kill it and the seeds last a while in the ground. Their recommendation was to spray the entire lawn with glyphosate and re-sod. I haven't done that yet, don't know that I will. I've considered painting the individual plants with glyphosate with a small brush but it is pretty wide spread. I don't know that I have the patience to do that. It would be a long process.
Triclopyr. I never use it because death to trees. But...between the violets and speedwell I am thinking this is the year.that's one of those flowers that came in here via a wildflower seed mix. really difficult to eradicate once established.
in gravel like the above i have to go through several times and stir up the entire area and then wait for the new sprouts to emerge and remove those and then keep at it. can take years.