Oh, I see. Thanks for clarifying!

You will need to go to those other categories (where you accidentally added that particular word) and delete the word from there (use the "X" delete button below that category's word list). In this case you can't delete the duplicates of that word all at once, since you need to take it out from each category where it was added last time.
Once you've deleted the copies of that word, you can go back to the category you were editing and you will see that the Word Library only has 1 instance of that specific word.