I'll admit that I wasn't particularly engaged with this episode for the vast majority of it. Heck, I spent the first 20 minutes trying to figure out who Rigsy was and why he would have the Doctor's telephone number for emergencies.
So, a LOT of the last 15 minutes went over my head. The two-headed mother was in a medical stasis. To free the mother, someone needed to use a key to open a panel on the statis controls. Somehow, the lock was supposedly identical to the lock on the TARDIS even though Me hasn't even ridden in the TARDIS from memory.
Also, the Doctor had a key to the TARDIS even though he now opens the doors by clicking his fingers (or was that done away with in a previous episode, much like the Sonic Screwdriver). Clara has a key, but for some reason she didn't unlock the panel even though everyone (or was it only the Doctor and Rigsy) knew that it was some kind of "trap" set by Me.
All of that seems awfully convenient. I guess that Me's mysterious accomplice could have designed the trap with knowledge of the TARDIS, but it all seemed a bit bizarre and they rushed through it as though they knew it made little sense.
And then we get to Clara's tattoo. So, even though Me has complete control over the tattoo when it comes to Random Old Man Thief and Rigsy, once it is transferred to Clara she no longer has any control? I can kind of accept that, except the fact that the Doctor is defeated and Clara is killed because of "contract law" is odd in the extreme.
Even if Me couldn't re-absorb the tattoo, I completely missed why Clara couldn't pass the tattoo to Me (especially since Me promised to protect Clara and Me is immortal) or why the Doctor simply didn't insist on Clara passing the tattoo to him since at worst it would cause the Doctor to regenerate. Surely the Doctor would be willing to regenerate to save Clara's life? Was Clara somehow prevented from passing the tattoo to Me or the Doctor? Was it once again due to contract law?
Anyway, it's not that I mind Clara being killed. A "happily ever after" ending for every companion is a little unrealistic. And I'm not even fond of Clara as a companion, other than her appearances as Dalek Clara and Victorian Clara. But, I still think as such a long-standing companion, Clara deserved a better send off than some nonsense about a killer tattoo. I would have been happy to see Clara die sacrificing her life for others. Or even due to her own arrogance after she bluffs her way into a dangerous situation pretending to be the Doctor and completely fails.
But, I really didn't understand the purpose of this oddly nonsensical death. Especially for a bit character like Rigsy who they tried to make appealing with a newborn baby, but who wasn't all that engaging on screen.
Anyway, I expect that Clara's story will be revisited at some point. After all, there are millions of different Claras still scattered throughout the Doctor's lifetime isn't there? Or was that undone at some point?