The "defense" is that if the officer was not on duty while at the gas station, then the murder is not eligible for capital punishment.
The Texas Penal Code specifically defines capital murder as murder which involves one or more of the following aggravating factors:
murder of an on-duty officer or firefighter,
in the course of committing or attempting to commit a certain felony offense,
Murder for remuneration,
while escaping or attempting to escape a penal institution,
while incarcerated with a qualifying factor,
Murder of an individual under ten years of age, or murder of a person in retaliation for,
or on account of, the service or status of the other person as a judge or justice of any court.
The defense is going to try to say Deputy Mils was not "on duty" since he was meeting a woman at the time of the murder. That is going to be a hard sell in Texas since the murder was caught on video and the officer was murdered execution style while pumping gas.