I would try a stud extractor first... carefully grind off the surface and make sure you centre punch the centre point before drilling a pilot hole. Use a new/ sharpened drill and take your time as, if you cant extract the damaged part, the threads will be intact. A stude extractor is a simple left hand threaded tap with a coarse thread and the theory is this will jam in the pilot hole and wind the damaged part out... in practice, they dont always work. As the threaded part appears to go all the way through, it may be possible to 'screw the damaged part all the way through t the other side... you could drill a pilot hole and use a self tapper to do this. I would soak the threads with duck oil first and even use a tiny cold chisel or punch to drive to turn the part.... it can be done but needs time and care... hope this helps.
Steve