I normally will leave them to die out, the trick is making sure the roots are fully killed, and I believe letting the weed b gon settle in is the way to do it. However if you didn't put preemergent down you might want to do something to collected a those white seeds that will start to grow new dandelions.

I try to get the weed b gon on the dandelions before or as soon as I see yellow. Once you see white the seeds are ready to spread.

Thanks! So you don’t do anything after you spray? Do they just disappear...? LOL

Yes, they wilt and die in place. You do not need to pull them out. If anything, the "deadelion" becomes organic material for the soil. You will have recurring weed problems, though, unless you can manage to thicken up the grass. You might consider reading through this forum about good practices for a healthy lawn.

Spring isn't the best time for reseeding, but in this small patch I would consider throwing down some fast growing annual rye. It germinates very quickly and will help crowd out any weeds in this thin area for the rest of the growing season. In the fall you could reseed with something more permanent.

Be aware that dandelions have the ability to set seed even after the plant has been uprooted, weedkilled or cut down even from unopened buds. All those dandelion clocks in the picture can still spread their seed so expect a new generation to grow. Next time try to deal with them before they even produce flower buds.