KB3035583 / GWX.exe and all that stuff

There have been lots of threads about Microsoft sneaking in KB updates that give them the power to show those annoying Win10 pop-ups. To be fair I found a thread just now where a contributor said he needed to have them, but most have moaned - I think.

I'm now getting full screen "Get your free Win10 now!" pop-ups all the time; having uninstalled the above KB and also having followed other advice given in the forum I've been trying to establish what's caused this pop-up.

I now think it's GWX.exe; this has found a way into my PC - I've no idea how. Can I safely remove it?