Dear Chuck,

I believe you have correctly identified this parasitic plant, also referred to as Dodder.  It is indeed fast growing, and definitely an issue.

You do not say if this is embedded in plants you want to keep.  For the home gardener, I recommend hand pulling immediately.  All of it.  This is a complex organism living off of other plants and is able to regenerate from the host plants.  

The best way organically to remove them is to pull them out, rake or shovel the area to remove all plants and roots.  

A pre-emergence herbicide can be spread in the spring to stop any further seeds from germinating in the area.  It has a long-lived seedbank and tremendous growth potential using the nutrients manufactured by its host plant.

Glyphosate is an option as well.  This will kill all the living plant material you spray it on.  It will penetrate to the roots and the plants (all plants) will die.

Your pictures show that seeds are already being produced.  I would recommend removing all the plant material as soon as you can, bag it and put in the trash.  And continue to watch for any shoots coming up.  Pull them immediately.

I hope this has helped you make a decision.  If you have further questions, please contact us again.