This procedure assumes you've taken the connector off - not an easy task but one I have not yet developed a procedure for. I just yanked it off but I hope to study this and update this post.

So here goes:
The -8570 starter relay is a 4P, it's held on by a 10mm bolt through a nut welded onto the other side of the bracket that the bracketed relay bolts into.

Thus all we need to do is take a small ratchet (large might also work, I'm not sure) and unscrew the bolt off. The only problem is there is a tendency for the screw to ratchet back to the tighten direction while we ratchet for the next unscrew. To get around that, just squeeze your left-hand up next to your right-hand and hold it on the socket, thus the socket in turn will hold the screw from re-tightening as we ratchet on the loosen. I made a movie of this procedure and have included a still from it here. So the camera is lying on it's back on the bottom of the car's floor.

Another advantage to having the hand there is we can catch both the relay and the nut when they fall at the end.

For me, this procedure worked perfectly and it will allow me to more easily put it back onto a wire harness.

At first, I wasn't sure whether it was a phillips screw, a bolt, or a combo bolt-screw, so I put my hand up there and felt, and I also noticed that a screw-driver slid over the face of the nut. A mirror would also help here.

So if you need access to the relay to understand how to remove the connector, you may find it easier to remove the bolt first and take down the relay with it's harness attached. I have not tried to do this procedure WITH the harness on (would be harder than with harness off, probably much harder). I haven't tried that way yet - might try this some time.