UnkyUB, you might find this interesting :-
http://myinkisnotlow.com/index.php?option=com_content&task=view&id=19&Itemid=2in particular the paragraph which reads as follows :-
"You can disable all printer Warning Messages by disabling ALL communication from the Printer back to your PC. To
disable ALL communication from your Printer to your PC, do the following:
From the WINDOWS™ START Menu, Click on “Settings → Printers”
RIGHT CLICK on your Printer Model, and Select “Properties”
From the Properties Menu, Click on the “Ports” Tab
Un-Select the Box that reads: “Enable Bi-Directional Support”
Click “APPLY” then click “OK” to exit
NOTE: This operation will disable ALL COMMUNICATION being sent from your printer to your PC, including paper out,
paper jams, low on ink, etc. For All-in-One printers, this will ALSO DISABLE CERTAIN OTHER FUNCTIONALITY SUCH
AS SCANNING. This operation can be reversed by repeating these steps and checking the “Enable Bi-Directional
Support” Box. "
I know that it states above about this having the effect of disabling scanning in an all-in-one machine, but if I remember you HP is a printer and not a multi-job