You won’t even notices them after a couple mows. I’d leave them. Digging them up sounds awful. I can’t tell how tall your grass is, but if you’re mowing on a lower (shorter) setting, you may want to move to a higher setting. Higher grass will make it harder for weeds to compete, and it will hide those dead dandelions. 😉

I would try to take them out by mowing. For the extremely large (obviouis) plants I may dig them. If after a year or two and you still have quite a few, I may treat the area with a broad leaf weed killer. Again depending on the number you may get by with a spray that you can put on the individual plants

Consider removing viable seed heads en bloc w/o disturbance.

For future: flowers ( seed precursors) can be removed during rain, as long as no electrical activity overhead ( if pre-emergent not in place).