Hi Dch48,
My good friend, did you check your version of it against this:
http://www.backgroundtask.eu/Systeemtaken/taakinfo/42800/EndProcess.exe/As it is being considered a PUP, we searched for MD5: fb9f5efc10280f3659dce48069725c3c
The file has no own spreading routine, it is a low risk, low distribution potential and has low damage potential. The only malcious use here you could think of is that it could be used by rogue users or malware to lower security settings. What this potential comes down to can be found here:
http://www.threatexpert.com/report.aspx?md5=fb9f5efc10280f3659dce48069725c3cStill being detected as PUP. You could upload and report it here as well:
https://www.webimmune.net/default.asp but they will have a reason to keep it in their database.
I would not worry about it now as you have checked your version and know it will do no further harm and know why it is there and what it does - it is the Factory Reset Application of HP and running as a background task. As far as has been established in this thread this EndProcess.exe is a safe one,
polonus