See "Redress Control Number"
This is for "correction of errors", not for an actual challenge.
A typical error was matching on a common name. A classic example was Ted Kennedy: his name was used as an alias by someone actually on one of the lists, and he was denied boarding.
This was back in the early days when the airlines were responsible for the matching. Now, the TSA does the matching and feeds the info back to the airline, and the redress control number is how you "correct" it.
It doesn't change the presence of your name on a list -- it just give you a "key" to be excluded from a match.
The goal will be to get as many on that list as possible & to make it next to impossible to remove a name. All it takes is mountains of red tape and an expensive legal process.