The only solution (as it appears on the HP Support forums) is to uninstall the program. If it refuses to uninstall, then you can force it and luckily, there are plenty applications developed for this purpose.
Try using Revo Uninstaller. Even if it can't uninstall the application normally, it will force it to uninstall by wiping out all traces of its presence from the system.
Reboot the PC, then start Revo again and look for HP Welcome in the list. It shouldn't be there, but in case you find it, right click it and Force Remove it.