First, we need to identify the offending thread that is usually extruded or causing issues like redness, swelling, pus discharge. It would be best for the treating doctor to be the one removing it as he knows the depth and area of placement.
Then we will inject local anaesthesia, make a small incision, grasp the thread with an artery forceps and remove it with firm pressure.
The difficulty is in isolating the thread via a small incision. The removal of the thread can also be quite uncomfortable for the patient.
The best way of treatment is prevention - please look for highly experienced thread lift doctors/trainers and not just let low prices be the primary factor as thread lifting is an extremely difficult procedure and complications are extremely hard and troublesome to fix.