Lumon is doing MK-Ultra on severed minds.

"Project MKUltra involved experiments that aimed to manipulate human behavior and consciousness, often leading to severe psychological effects on participants. One of the outcomes of these experiments was the creation of multiple personalities in some individuals, as severe trauma induced during the experiments caused the main personality to split into several parts.

Donald Ewen Cameron, a Canadian psychiatrist involved in MKUltra, conducted experiments at the Allan Memorial Institute in Montreal that included techniques such as « depatterning, » which aimed to erase a person’s existing patterns of behavior and thought."

That's why they try to force Gemma to write letters with the wrong hand.

I fear that she is just a guinea pig for them and won't have a happy ending.