Here's what I was able to do and it worked well and quickly on my '21 SL5 with 1500 miles:
1. Made sure I had a good 1620 battery - Even though they are still sealed in retail packages, they are sometimes dead when you break them out of their polyethylene prison.
2. Grabbed a pi\air of my wife's make=up tweezers (I think they are eyebrow tweezers. Very Sharp and angled at the end.
3. Covered the ends of the tweezer with scotch tape - folded over each and trimmed to 1/16" on the sides.
4. Grabbed a dental pick, but that was too thick, Had an old pick from a watch kit, so used that, but turns out I didn't really need it.
5. Torx T10 and remove screw for TCU cover
6. replace screw in hole loosely
7. Unplug TCU from harness (GENTLY)
8. Take TCU into house with better light and workbench for elbows
9. Using shielded tweezers, squeezed metal clip that holds the battery, up, and it clicked and seemed to lock in place.
10. Used slim watch prong gently on side of battery to spin slightly. Battery spun easily.
11. Flipped TCU so battery port opening was upside down and pounded my palms together while holding TCU in my hand and battery started to come out.
12. Gently pounded my palms together 1x again and the battery was about 1/4 out - enough to grab it with the shielded tweezers and gently pull it out.
Honestly, at first, I felt like I was taking apart an atom bomb, with all the warning about shorting the battery and TCU out. But it woorked out fine and went back together even easier.
Best Wishes everyone!!!