The other issue is the worm itself. The end appears to be rounded, presumably as a result of wear. Ideally the ends want to be flat. If it is not hardened then you can simply face off each end in the lathe. Wrap a piece of aluminium, brass or copper around it to protect the worm from the chuck jaws. A piece of 22mm plumbing pipe split lengthways for example.
If hardened then you might be able to mount something like a Dremel on the toolpost to face it off using a grinding stone. You could also use a disc or belt sander, you would just need to come up with a suitable way of holding it square against the disc or belt.
If hardened then you might be able to mount something like a Dremel on the toolpost to face it off using a grinding stone. You could also use a disc or belt sander, you would just need to come up with a suitable way of holding it square against the disc or belt.