Hello Tom, 

Thanks for reaching out to the EMG helpline! 

I believe you are observing purple carrot-seed moth caterpillars on your dill and fennel. These tiny caterpillars feed on the flowers of plants in the parsley family, which includes your fennel and dill, along with caraway, carrot, celery, coriander, cumin, and parsnip. They will feed on the flowers of host plants and create webbing around them, making it very difficult to collect seeds from these plants. 

Sprays may help to control smaller caterpillars. In addition to the neem that you have been applying, you could consider the application of Bacillus Thuringiensis (BT) or Spinosad/Entrust. Once the caterpillars are bigger, the best control will be handpicking. Always follow the label on the product you're using. You can consider applying sprays at times when bees are less active, typically in the morning or early evening. 

Here are a few articles with additional photographs and information about these caterpillars:
https://blog-fruit-vegetable-ipm.extension.umn.edu/2022/08/saving-seeds-look-out-for-this-new-non.html

https://extension.umn.edu/yard-and-garden-news/non-native-insect-watch-purple-carrot-seed-moth

https://bugguide.net/node/view/432767/bgimage