Answer: Based on your description it sounds like you have either a vining type of weed growing in your flower box or perhaps the rather peculiar rootless pest called dodder. Either one certainly could smother your plants. The best approach is to continue removing it regularly. If it is a rooted plant, try to pull the entire weed system with it. Alternatively you could temporarily remove the impatiens, grub out the weedy vine completely and then replant the impatiens.
If it is dodder (looks like brown or golden thin spaghetti), remove it and certainly do not allow it to set seed. This plant begins with roots and can be controlled by cultivating the soil to disturb it as it germinates. (A thick mulch can also help.) However, after germinating dodder becomes a parasite no longer dependent on roots, so the only thing to do is to remove it by hand. If it is dodder, you may wish to dispose of the soil in the box altogether -- but out it in the trash, do not compost it or dump it outdoors!
Good luck with your weed problem!
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