Do not let it flower, if it does, cut off the flowers before they dry and the seeds can be released. If the plant is small, wet the ground around it, it is easy to pull when the plant is small and the soil is wet. If the plant is larger and you can't pull it (it has a long, strong tap root, I found the only way was to use something like roundup. If it is in the lawn, the one safe for grass works well. I cut it off close to the ground and direct the solution onto the raw stump so it is close to the roots and absorbs into them quickly and will destroy the roots in one treatment. I get all sorts of weeds from my neighbors yard. The top half never gets cut, so I get every weed known to man in my veggie garden and upper yard that borders the top half of her yard on one side. The top border of my yard has a chain link fence also, but the neighbors behind put up a privacy fence around the above ground pool as is required here for pools. That foot between the fences is a mess with weeds also that spread into the yard no matter what is done.
Make sure that you take care of any plants that have flowered first. It could be a sticker was right by it and got planted when you disturbed the soil and a new plant came up. Until all the seeds are gone, you may get more. I have seen thistles with roots as tall or taller than the plant. Be patient and take care of them when they are small and eventually they will be gone unless a bird or critter drops a seed in the yard.
Hi Harriet. I'm Cindy. Unfortunately the only way I know to remove thistle is to pull it out roots and all. Spritzing the weed with water will really help with pulling it out. I had to learn this lesson the hard way when I hung a bird feeder filled with all thistle. The birds loved it, especially cardinals. What a job that was. Good luck Harriet.