Thoughts from a not-and-never-have-been-a JW (so I suppose I'm not an apostate in JW terms, just an ordinary satanic and worldly person):
My first thought was to ignore it, especially as (if I got the right impression from your post) your friends and colleagues know what she said to be a load of crap, as to do anything at all might just keep it all dragging along.
On further reflection, though, I think it may be worth taking some action because sometimes issues such as these can be very destructive in the workplace and you don't want to have to spend your time correcting false information being spread about you. Also, I get the impression that sometimes JWs are not very capable of rational thoughts and actions but can be good at presenting a (false) 'reasonable and concerned' persona.
My suggestion would be this. Prepare a brief note of what happened containing the details of what was said by the JW and to whom. Prepare a short (written) note to the JW saying something like 'It has come to my notice that you have told untruths about my personal life to my colleagues. Please do not do this again.'
Speak to your boss/manager. Explain what has happened. Give your boss the brief note and a copy of your note to the JW. Tell him/her that you hope that your request to the JW will end this problem and that you don't want any action taken unless it happens again. Ask him/her to keep the notes on file.
Hopefully, your note to the JW will put a stop to this. If it does, you have solved the problem, shown yourself to be reasonable and non-confrontational - but not a doormat. If it doesn't and further action has to be taken, the fact that you have ensured that what has happened is on file, and that you have tried in a reasonable way to deal with the issue, will make it easier for any more formal action to succeed.
Or you could write to the Jerry Springer show and pull her hair out on TV ....
Good luck.