Hey Chris...
Don't know much about your Jeep (year/model, etc)...
I have an '04... also have the Factory Service Manual for it (Thanks Treefrog... hehehe... it is my Jeep Bible now... next to parts catalogs).
Anyway... back on topic... according to the factory manual mine is not servicible, only replaceable...
But that is factory... if mine is the same as yours it is only clipped in... disconnect the hose and pop it out.
After that... maybe soak it in rubbing alcohol or WD 40... not Jeep related, but I have a bowling alley machine I use at work that has sprayers which routinely clog, and that is how we unclog them... the chemical that clogs it is similiar to washer fluid... we soak them over night, then hit it with compressed air backwards (so as to not blow out the fine tip).
Hope this helps.