Theodore Wafer's lawyer, Cheryl Carpenter, is trying to give jurors a negative image of Renisha McBride.
She wants them to see pictures on her cellphone and her old Twitter account, called "Young 'n thuggin'."
"We have reasonable grounds to think something in her Facebook and Twitter is relevant to case to show she was the first aggressor," said Carpenter.
Wafer said he fired in self-defense, thinking McBride was trying to break into his house. He admits to shooting her with a shotgun when she stood on his Dearborn Heights porch in November 2013.
McBride closed her Twitter account more than a year before she died.
"This is not relevant. This is not admissible. This in no way shows any kind of reputation evidence for Renisha McBride," said Athena Siringas, assistant prosecutor.
Judge Dana Hathaway repeated her ruling that McBride's social media history will not be allowed into evidence.
Jurors saw the pistol-grip shotgun Wafer used to shoot McBride. The defense is trying to show that the force of McBride's pounding on Wafer's door forced a screen insert out of position, one reason why Wafer was afraid.
However, Michigan State Police firearms expert Shawn Kolonich believes the shotgun blast caused the screen door's damage.
"I've run into screen doors before and knocked them out myself, so I know that they're not in there with a great deal of force. They're not designed to stop things, except for bugs," he said.