Mow. Make sure you collect all the cuttings in your lawnmower bag and discard them at your local composting dump. It's all you can do.
Alternatively, just enjoy them! Seriously. Dandelions are beautiful flowers and insect-friendly. If they were rare everyone would want them. We have Cat's-ear as well as dandelions plus pignut, whorled caraway, wild angelica, knapweed, Herb Robert, Herb Bennet, Heath bedstraw, tormentil, various speedwells, hogweed, sorrel, lady's smock, lesser celandine, devil's-bit scabious and many, many more.
I thought it was all the rage to encourage wildflowers 🧐