I would remove the device from the wall, separate the plastic device from the metal frame and stuff it, with the wires still connected, back into the hole in the wall.
I'd then get a blank cover plate to secure over the hole and paint to match, or whatever.

Randy, if I understand you correctly, unscrew the Leviton metal frame, separate the plastic middle and put it back (including attached wires) into the hole. Is there any danger touching this thing?

I would like to not have any cover plate, painted or not, if I can avoid it. I'd like to patch, texture and paint, unless that seems unwise. I'd remember where it was. That being said, I'd prefer a flat painted plate to the wall phone base that currently sticks out from the wall.

Since this wall mount jack is also obviously being used as a punch down distribution block to other wired connections, you need to retain some sort of access to it.

I wouldn't try to break it away from the metal frame as the plastic may break and cause some connection problems. But as Randy alluded to, leave an accessible painted blank wall plate to provide future access if needed.

One very important point to consider is that you should always have a hardwired telephone for communications during a power outage.

In our kitchen, after a remodel, we did a 1940's stainless steel retro-style wall mount phone which looks really cool and provides the hardwired connection in event of a power outage.

It is safe to touch the wires.

I think once you get that metal baseplate off the wall, you should be able to see if the plastic part will separate easily. I bet it will.

Okay, the wires are safe to touch and I shouldn't plan to close up the wall entirely.

A flat plate looks better than the existing one, but it's just a flat plate. At least the wall jack a few posts up still is functional. How do I go from the one below with the jack sticking out to a flat plate with the jack recessed.

linelle,

The second photo you posted is a wall plate jack for simply plugging in a regular telephone cable. The third picture, which is what I assumed already you were talking about, and is for a wall mount phone which is also mechanically supported by the two large screw heads.

From your first picture I did not notice at first that it appears the plate is installed in a metal single gang electrical box. Even if the plastic portion easily separated from the metal plate, I'd be concerned the box could short across the connections.

Either wrap it in electrical tape before shoving it in the box, or better yet, have somebody remove it the jack, crimp the appropriate connections back together using "telecom splice connectors" and then install a blank wall plate on the box.

The appropriate connections are from the solid color wires at the top, to the two striped wires directly under each one shown in the first picture.

yosemitebill, please don't think that because I'm confused your advice isn't very much appreciated. :)

In case I didn't make it clear, I don't want a wall-mounted phone. If covering the phone wiring innards with a blank wall plate is better than covering it up with sheetrock, I'd just as soon keep the jack available. It's actually a better location for my base station in that I'd see if I had any messages, rather than nipping into my office. The main issue now is this wall unit is UGLY. I'd much prefer a lower profile jack, maybe even a smaller one. It's just in an awkward location and I'd like to minimize its profile.

Sure, you certainly can change it to a standard wall plate jack instead. You'll need to a wall plate jack with screw connections on the backside. It'll already have red, green, black, and yellow wires attached to each screw terminal.

Remove the existing plate, and using your picture as a guide, match the colors of the striped wires to the solid wires at each screw terminal.

If you're unsure of doing this, you may just want to call somebody to do it for you.