After he killed her with cable ties wound tightly around her neck, he sent a text message to her younger sister, which read: "By the time you get there it will be too late."
When Sarah asked him where he was, he replied: "We all know it is too late for that."
Out of fear for Becky's safety, her distraught sister ran to her home only to find Becky strangled to death in the tub.
Police were called and Smith was arrested on the suspicion of murder. Smith admitted to killing Becky, who was six months' pregnant with another man's baby. But said he was out of his mind when he did it.
Just over two weeks before her death, Becky had contacted the taxman to report a change in circumstances within the household and to tell them that Smith had moved out.
As a result, it was calculated that Smith had been overpaid by £1,527.21 in tax credits - which needed to be repaid - since he left the family home just after Christmas in 2014.
"According to Shane Anderson [Becky's new boyfriend], the defendant was always trying to get Becky to go out with him and his family despite her telling him repeatedly that the relationship was over and there was no more him and her.
"In Shane's view, the defendant did not want to see Becky happy and was very jealous."Mr Caudle added: "He [Smith] tightened cable ties to her neck to a degree that they could not be seen and he murdered her.
"Maybe because of jealousy that she was pregnant with a new boyfriend, maybe that combined with she had told taxman he was no longer around and he no longer had tax credits, we don't know."
Smith was sentenced to life in prison but he showed no emotion when they handed the sentence to him.