Since I last wrote I’ve helped a few more clients with the HP printer problem. It seems that, for the most part, this has been fixed. If you are still having issues, try the following:

Delete the HP printer files from your user library
1. Go to the Finder (by clicking on the Finder icon in your dock, or just click on the desktop).
2. Hold down the option key while clicking on the “Go” menu (at the top of the screen, to the left of the Apple menu), and click on “Library”.
3. In the Library window, open the Printers folder and delete any HP drivers you see. If you see an “hp” folder, delete that too.
I haven’t done thorough research to see if these next few steps are necessary, but I have found, with two clients, that they were necessary to stop the warnings about HP drivers popping up.
1. Go back to the “Go” menu. Click on “Computer”.
2. Open your hard drive. It’s probably named “Macintosh HD” but you may have renamed it.
3. Open the Library window, then open the Printers folder and delete any HP drivers you see. If you see an “hp” folder, delete that too.
Open System Preferences.
1. Click on “Printers and Scanners”.
2. Select your printer.
3. Click on the “-” button below the printer list to delete the printer. Click on “Delete Printer” in the dialog box that asks you to confirm you choice.
4. Once the printer is gone, click on the “+” to add the printer back.
5. In the resulting dialog box, choose the HP driver in the "Use:” dropdown dialog.
6. Click on “Add” in the lower right.
7. Your computer should now go and get new drivers from Apple.
When this is finished, test your printer.