First thing first. Wipe clean the lens.
It didn't help.
Apparently some water got inside the camera. I decided to replace it.
(0) preparation
Replacement parts: Dorman OE solutions 590-956 Park Assist camera (approx. $84)
Tools: minus screwdriver
toolset with rachet, with 10mm and 3/8 inch (? [forgot exact size]) screw sockets
Time: 15-30 min
(1) remove liner of trunk lid
The liner is fixed by several push tabs, two rubber knobs, a plastic cover for trunk ratch, and a plastic part with a handle.
Pull and remove push tabs. Slide, pull and remove rubber knobs. Pry, pull and remove ratch cover. The handle part has two doors that hide screws. Pry open the doors, and unscrew the hidden two 3/8 inch (?) screws. Then you can remove trunk lid liner.
(2) loosen chrome bar that houses back-up camera and license plate lights
There are four screws and two push-tabs that hold this part in place. Unscrew two 10mm screws from inside trunk lid. Then look at two license plate lights. Slide and remove these two license plate light housings. Then you can access to two hidden 3/8 inch (?) screws. Unscrew and remove them.
From inside trunk lid, you can see two plastic tabs with "minus" head. Push them with a minus screwdriver.
Now you should be able to pull away the chrome bar a bit (2-3 inches) from the trunk lid. There are cables and wiring inside the chrome bar; that is why you want to just loosen it. Don't risk damaging the cables by yanking the chrome bar off.
(3) remove old camera
The camera is connected to cables with a connector on your left. Disconnect the connector of the camera. Then check the camera part. There are two tabs that are holding the camera part in place. Use minus screwdriver to push these two tabs on the right and left sides. Pull the camera part toward outside and remove it.
(4) install new camera
Send the connector part in through the square window, then push the camera part in. Connect the connector to the cable. Secure wiring in place.
(5) Put back the chrome bar and test the new camera
Push back the chrome bar, while adjusting position of its water-resistant lining. Once the bar is in place, put back and tighten the four screws. Put license plate light housings back in.
Then, close the trunk lid, get in the car, turn on the engine and shift the lever to "back". Check the image on the rear-view mirror and its quality. (my car is non-navi, and backup camera image appears on OEM on-star rear-view mirror. Your setting may be different.)
It should be good as new, or maybe even better than OEM camera.
(6) Put back the trunk lid liner and you are done.
I searched this "how to install/replace back-up camera, Cadillac CTS 2008-2013 2nd gen sedan". There was no detailed DIY report or video. So here it is. For my own record and for 2nd gen CTS drivers who need to replace the camera.
Hope this helps.
[Old OEM camera]
If you are clueless about minor DIY on your car, BestBuy's Geek squad can install back-up camera for you. Or, just ask your dealership.