From the picture it looks like some sort of coarse grass. Plants with leaves where the veins in the leaves all run parallel are either some sort of grass or something like a lily, onion or narcissus where there is a bulb underneath, have you tried lifting a bit to see if there is a bulb? Where did you get your turf? Some suppliers are not too particular. The trouble with most selective weed killers is they rely on the shape of the grass leaf to slide off it, so they would slide off those leaves too. If it is coarse grass mowing it regularly would allow the better grasses to take over usually. My experience is that when people sow special grass seed that, unless they use a cylinder mower and treat the lawn with care, within four or five years the grass suited to the ground takes over. If you lift a plant and there are simply what look like grass roots underneath, no bulbs or corms, you could try simply slicing the 'turf' off with a spade after you have mown, turn it over to bury the 'weed', and sow some decent grass seed onto the bottom.
