I'd cut them or roundup them, never weed eat them. A weed eater can do a lot of damage when it unintentionally folds over the coil fins.
“I am for doing good to the poor, but...I think the best way of doing good to the poor, is not making them easy in poverty, but leading or driving them out of it. I observed...that the more public provisions were made for the poor, the less they provided for themselves, and of course became poorer. And, on the contrary, the less was done for them, the more they did for themselves, and became richer.”
― Benjamin Franklin
Jokes aside those are service indicator vines. I plant them on all accounts. Then you tell the customers if you cannot see the units it is time for service. I just looked at the instruction book that came with the seeds and judging from your picture in about two more weeks those units are ready for service.