The episode is set in 1961 and the baby is born via c-section so the mother is not awake to see the baby being born. The baby is just taken to the room where bed pans and such were emptied and I wonder if this really did happen? Were babies just left to die by themselves?
While I can't offer an exact answer to OP's question, I'd like to add some context to those who might not know. Thalidomide began to be used as an anti-nausea drug and a sedative, particularly for pregnant women, in the late 50's. The drug's effects on most people is mild, but unfortunately it can pass through the placenta into a developing Foetus.
I won't show you any pictures because of how gruesome it is, but babies were born with numerous deformities, particularly involving the limbs, and many did not survive. It caused substantial numbers of birth defects and subsequent deaths in many Western countries, including the UK, Canada, and its origin, West Germany. Thankfully, it was rejected by the American FDA and so the US did not experience Thalidomide like other countries did, though it still passed into the public imagination, and was a substantial spur for the expansion of drug regulation in the West.
Slightly anecdotal but upon seeing this episode, I asked my Gran who is 90 whether this was a thing. Absolutely yes, they did. When my little sister was born, she was 1lb 8oz and my Gran was terrified, because when she was young very much the same reality that applied to deformed babies was applied to tiny babies. Often babies were just left in the cold, to die of natural causes as a mercy, to save them from a life of pain or hardship. Mothers would rarely be told the truth, and sometimes were just told the baby was stillborn.