how do you remove a gatehouse door knob with no visible screws

It can be a captive knob - permanently attached to the spindle or to the backplate a.k.a. rose or rosette.  If it's attached to the spindle, it would normally come out of the latch with the spindle once you removed the opposite knob.  Maybe there's rust or gunk that's keeping it in? A slight knock with a mullet would have moved it. If it's fixed to the  rosette, the latter would have screws that you remove and take them both out.

See if you can snap a picture and post it here. The "+Image" link at the bottom of this form lets you upload a picture. It would make remote troubleshooting much easier. 

I prefer the brushed nickel or oil-rubbed bronze. The brushed nickel hides wear and tear very well. And the oil-rubbed bronze just looks amazing.

You need an allen wrench. I have a gatehouse mushroom type knob with a pushbutton lock. There is a recessed screw that needs to be turned counterclockwise.

I also am trying to remove a Gatehouse entry lockset with no visible screws. I can get the strike plate cover off but not the bolt. It will not release more than halfway.

On the bottom side of the doorknob or lever is a small hole. With a probe (allen wrench, small screwdriver) that will fit through this hole (on the inside knob) push upward. This will press against a spring loaded latch that holds the knob in place. As you press upward, pull outward on the knob. With indoor knob removed unscrew the cover plate, exposing two Philips screws that hold the assembly in place. Video:

I got the lock off ,trying to remove the handle. There's no screws or allen screw