"Retro-tatting" is the humorous term for picking out stitches or untatting. When we find a mistake a ways back, there is the hard decision whether to pick out stiches all the way back, or just cut off the work. I am surprised I never hear anyone talk about the rapid method for retro-tatting.
What you have to do is unwind the thread off the shuttle and pull the core thread out through the stitches. On a chain, you can get a grip on the core thread at the base of a ring, or under a picot. To pull out a ring, start out sort of how you open a closed ring. Put a crochet hook in a picot and pull on the core thread until there is enough you can pull on. While pulling the core thread though the stitches, the thread end will twist and flail about, so be careful that it doesn't get knotted.
OK, it's a bit tedious, and not real fast, but we're tatters, and slow and tedious is what we do. Sometimes it beats picking out stitches.