There are several issues with your circuit.
1: The LMx39 has an open-collector output (as most comparators), meaning it needs a pullup resistor at its output. In your circuit, this is implemented with R20 + R5. It works, but is not optimal.
2: With R12 and R13 you have an immense hysteresis, namely half the supply voltage. I'm not certain if this is what you want.
3: You give no indication of what voltage is present at "K1 4". This makes it difficult to help.
4: Yes, you can eliminate R12. The combination of R21, R22 and R3 will give you hysteresis, but it will vary with the position of R3.
Several issues are unclear here, but your circuit is really not good.