Omg. I googled the vine that grows in my driveway and makes little tiny plant seed versions of this device and learned that it is in the Caltrop family!
I literally salt and vinegar the ground after ripping it out. I don't burn it, since I live in California and burn piles are generally frowned upon (but are allowed a few times per year). I send it off to the municipal compost, where it does at least get somewhat cooked. Then I go over it with one of these bad boys to get any stragglers: https://stickerburrroller.com/product/sticker-burr-removal-tool/ Doesn't matter, they come back strong several times per year.
Same thing with blackberries up here. Once they get established they're almost impossible to get rid of. At least they produce some berries once a year though. Those caltrops weeds are worthless in every way.