It's alleged staff repeatedly asked the group to leave, but were verbally abused.
The group is accused of then going to a nearby building site belonging to the company, where one person was working alone.
The worker told the group to leave, and then tried to push them out of the building.
Blair is accused of then spitting at the worker, hitting him in the forehead.
Peace Action Wellington, before today's court hearing, said they have the right to protest, and questioned if there was police bias.
The group had already successfully defended two cases this year, they said, and hoped to achieve a hat-trick today.
Charges stemming from a 2015 protest of the Weapons Expo were dismissed in February.
In June of this year, a judge also threw out a charge of trespass related to a protest at the Ministry of Defence.
Drew, who is representing herself in court today, said earlier her case should never have come to court at all.
"It's pretty disgusting that the police choose to unquestioningly accept the version of events put forward by companies and their employees, over the activists who protest their complicity in war crimes."
The police have repeatedly shown that they believe themselves to be acting for big businesses against protesters, rather than acting as neutral officers of the law, she said.
"The police said to me that they were going forward with the prosecution because we have a 'history of protesting'.
"That's blatant criminalising of legal activities that don't happen to suit them."
The case continues.