I'm not sure if this will work, as it might get reset by the jamf binary, or if its even the same thing, but you can try running the following command to see if it clears them
defaults write ~/Library/Preferences/com.jamfsoftware.selfservice.plist SelfServiceBadgeNbr -int 0
That key seems to hold an integer on the number of badge items the Self Service application displays, which I think should correspond to the number of Notifications inside Self Service. I have not specifically tested this theory though, so uncharted territory.
But, give it a try and see. Worst that could possibly happen is it won't work, or you may need to trash the plist and have Self Service generate a new one if it gets too mucked up. Best that could happen is that it will work, right?
EDIT: I meant to also say, you aren't missing a setting. To my knowledge the way they get cleared is by the user opening SS, going into the Notifications section and clicking the little "x" button next to each one to remove them. No JSS setting is there to auto clear them after a set period of time.
Resurrecting an old thread, my apologies, but I ran into this at my new job and wanted to note that disabling the option in the JSS, then running
recon appears to do the trick. I actually ran
manage first and didn't see the notifications go away. Then I ran
recon and didn't see it go away. Followed it up with
policy and finally after that it disappeared, though I wouldn't be surprised if
recon really fixed it but I was impatient.