I'm not quite sure about the word "sharpening".An extractor is not a cutting tool or a fish hook.
Typically,a new extractor will require a little bit of file or stone work.
An old,worn extractor? If you understand the extractor,there may be a place where filing will increase engagement,but it won't be the tip of the hook.
Where steel is worn away,you can't file it back on.Unless I'm very sure,the harder a part is to find,the less likely I am to boldly file steel off of it.If I'm in the mood to file,I might use the old extractor for a pattern to file out a new extractor.
Also,look at your brass. Rimfires and shotgun shell shave a small radius at the junction of the rim and case head. A sharp extractor can't engage there,anyway.It might be a mistake to assume the extractor should be sharp.
The hook needs to be undercut square,to engage the rim.
Unless the hook shows obviouswear,I'd be more suspicious of weak extractor tension or extractor spring.....or just grunge.