Do you have Adobe Installed? - not the free versions, the proper package. That certainly has that feature.
The other point is, if it genuinely is updating the web client of some software then the software package is already on the machine and the "damage" is done.
Accepting the download will not make the situation any worse than it already is - but you should get to know what is being updated.
You can either keep refusing and never know - or bite the bullet, which may not give you the answer you want but it will get rid of the NAG.
Usually I would recomend taking a backup before such a step but what is the point of restoring an "infected" system - it's better to start fresh (in my opinion). ;-)
Regards. Running a PC without backups is like driving a car without a seatbealt. Your knack'ed when you crash!