You may have a problem with this weed. I don't think your run-of-the-mill 2,4-D will control it. It may need specialty herbicides or selective application of glyphosate. If it goes to seed, you should also apply pre-emergent next fall.

I've never dealt with this particular weed, but have battled lots of others, and I'll say I think you should get rid of it ASAP, so there's no chance of it setting seed. Why not try an application a broad-leaf combo herbicide, in a few of the heavier spots? If it dies, you can gradually expand your treatment area, keeping an eye on how the new grass is reacting. If it doesn't die back satisfactorily though, I'd hit it hard with localized glyophosphate treatments, before the weather cools too much, or even dig up the areas where it's growing. That's what I had to do to patches of creeping bentgrass that came up with a new seeding of KGB/fescue I planted last year. In the Spring, you can reseed those areas.

If it has been mowed 2 or 3 times, you can hit it with something like redzone or three way ester herbicide to control tough broadleaves. If you haven't mowed it a couple times yet, you need to use something like drive or quicksilver.

jb nj
Don't worry about the weeds you have right now, concentrate in getting the lawn to grow into a thick turf. Experts recommend that this be done this way for the first season the grass is grown and later the next season, which is spring for you go after the weeds. It is hard to ignore weeds but if you do and feed the grass the lawn will be fine. Lawndivot 12