Barry's father already figured it out in a previous episide, when he visited his dad in prison and they had a conversation about what his father would say to The Flash if he could while exchanging knowing looks with each other. Notice his father didn't act surprised when he unmasked.
What if they convinced Eddie to have a vasectomy so he couldn't be an ancestor of Eobard? Although there would be some twist that he ends up adopting or becoming a stepfather so the timeline corrects events.