Answer: Based on your description, I think there may be a plant parasite called dodder infesting your Montauk daisies. I would strongly suggest you contact your local county extension for a definite identification of this and their recommendations on how to control it -- unfortunately it usually requires killing and removing the host plant and keeping a vigilant eye afterward. It is really something you do not want to have in your garden or allow it to seed about and spread. Here is a photo to compare with and some additional information.
Q&A Library Searching Tips