The real reason why Lumon has to kill Gemma

They need to run tests on her chip to test for synaptic recoupling, or reintegration. It's the only way to check if the severance barriers are holding. Cobel does this with Petey's chip to double-check if he was reintegrated.

There is no other objective way to check for this. Simply asking her if she remembers what happened is unreliable and subjective. And if you watch S2E07 closely, Gemma's expression shows that she very well may be lying.