Pushing to the front is impossible at first if the settings switch is still in place (see earlier comment).

Also, it’s worth mentioning that the steaming wand *will* come out with the right twisting and turning of the core. I got stuck her trying to figure out how to detach it from its hose. But the attachment is permanent. This is what led me to buy more maneuvering room by removing the settings switch with wires still attached.

There are two tubes connected to the water reservoir hole. The one in the first pic is the one that goes to the water valve, which is the one that you pull through to the top. The one in the second pic is the short one from the bottom of the pump that can detached from the water hole and left in place, to be transferred later to the new pump. Detaching it from the from the filter as shown adds to the impression that this is the tube to the water valve to be pulled through to the top in the next step, which the user quickly finds is impossible, it’s too short.

It’s better to keep the wires in place and remove the whole setter switch by prying off the knob, then removing the two screws exposed I was unable to remove the core your way because of the difficulty of getting past the setter switch, especially since at the same time you have to wrangle with getting the steamer wand out, even with the frother removed.

Also, your pic shows four wires to disconnect, there are actually five, and there’s no view of which of them go where—another reason for keeping them connected.