I uninstalled all things HP (except for the LT Scanner software. I was very nervous about getting rid of that since I could find no replacement. But I after I had uninstalled everything else and restarted my computer, TrayApp wasn't showing up anymore, so I thought it would be ok to leave it.)
Then I reinstalled the printer driver and the other HP program I had to uninstall, restarted my computer, and...viola! No more TrayApp.
Thanks so, soooo much!! I am soooo relieved to be rid of it!!!!!!!!!!!! Thanks!!