Hi HP8500JGH,
I understand that you would like to turn off your ink alerts. I will do my best to help you resolve this issue.
Controlling alerts on Mac 10.6
1. In order to control the alert messages on Mac 10.6 you need to go to system preferences and open the Growl icon seen at the bottom of System Preferences.
2. Once in “Growl” you will need to click on the Applications tab. Under this tab it should list an HP Events application with a check box next to it allowing you to enable or disable the alerts. You can also configure the alerts settings by hitting the configure button on the bottom of this screen.
3. For more specific alert settings select the Notifications tab in the Configure screen.
Applications Settings
Once done I suggest a restart of the computer.
I hope this helped, let me know.
Thank you.