However, Bridges later told media that, in fact, the petition had been deleted by an "emotional staffer".
"What had actually happened, I have learned this morning, was that a junior staffer was incredibly emotional on Friday night and took it upon themselves to delete it – we didn't know that until this morning," Bridges said at the time.
Anderton was in dispute with the National Party over what had actually happened and what media were told had happened.
He had reportedly retained Kensington Swan lawyer Linda Clark to represent his interests, though Clark would not confirm or deny this.
Bridges' handling of the matter has been questioned, including by former National MP and now independent MP Jami-Lee Ross.
"They [the staffer] are not junior, having served senior ministers and MPs for far longer than many in caucus have been in Parliament," Ross said.
"They earned respect through their service, knowledge and good judgment.
"They should not have been casually scapegoated in the media by the leader."
Anderton most recently was a press secretary for National, working with MPs in the agricultural and environmental areas.
He had also worked for a number of other National Party MPs over the years.
A spokeswoman for the National Party said the staff member had resigned from his employment with Parliamentary Service.
"While we would have welcomed him staying, we respect his decision to resign and wish him well in his future endeavours," she said.