Depending on your DE configurations -- probably if you use KDE or mainly KDE/qt applications (I'm on Openbox, but I have "export DE=KDE" on my autostart for some reason), or perhaps if you use tint2, HP systray applet may show up with non-responsive "stolen" icons from neighbor applications and behave oddly in general.
It's generally set to autorun by there being a file "
/etc/xdg/autostart/hplip-systray.desktop". All you got to do is to edit such...