Is this a new car to you? Was the lever already off or did you remove it? The reason I ask is it looks like there are some missing / broken pieces.
This is what the back of the release lever should look like
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In your third photo, it almost looks to me like somebody has tried to pry the lever off and has broken it leaving the guts of the lever stuck on the release rod.
If you read the service manual, you remove the lever by removing the hairpin style retainer clip. Once that is released the whole release handle comes off the rod easily. Getting the retainer clip off can be tricky. I have a thin tool with a little hook on it that I use to grab the loop part on the end of the clip. Some people have had luck working a thin rag behind the handle and using it to pull the clip off. Be aware that on some cars the retainer clip is positioned vertically rather than horizontally as implied in the diagram. My 2000 was vertical and it took me forever to figure out why I could not hook the retainer clip because I was looking for the loop where the SM said it was.
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I think that white plastic piece is the guts of your release lever and its still attached to the rod with the retainer clip. Use a soft plastic trim tool to push the interior trim away from the white plastic piece and you should be able to see the retainer clip. Remove the retainer clip and the white plastic piece should come off.
I don't know whether your release lever is salvageable. That metal clip in the 2nd photo looks like it might be the retaining clip for the lock cylinder. See if you can remove the lock cylinder because it is matched to your keys. I expect that you may be purchasing a new release lever and you will want to transfer the old lock cylinder to the new release lever - if you want to be able to lock the release lever.
