Pell was convicted in December over the rape of one choirboy and sexual assault of another in 1996. Last week, his bid to appeal the five convictions failed.
So far, two versions of The Chaser's amendments have been removed. But in what Mr Firth called a "mystifying" reaction, the church has seemed to deny these events occurred.
"The plaque of Cardinal Pell has not been defaced and the Chaser video was doctored on Photoshop," a spokesperson for the Catholic Archdiocese of Sydney told the Sydney Morning Herald.
"I'm mystified the Catholic Church has denied we've done it … There are videos of both times," Mr Firth said.
"It's almost like instinctively, whenever there's overwhelming evidence, they deny the whole thing. Like they have with the paedophilia going on in the church."
The videos show Mr Firth saying he is determined to "fix" the plaque, sticking on the new label first with blu-tac then superglue.
Mr Firth said his next plan was to learn welding and weld on another version.
SBS News has contacted the Catholic Archdiocese of Sydney about the matter but is yet to receive a comment.
According to the NSW government, the act of marking property can attract a fine up to $440, or, for an aggravated offence, $2,200 or 12 months imprisonment.
The Chaser's efforts have prompted a mixed reaction on social media.
Some celebrated Mr Firth's actions.
While others admonished him.
One user said, "whichever side you come down on, I think it's important to acknowledge those who have suffered, or are suffering, as a result of what Pell has been convicted of".
Those seeking information or support relating to child sexual assault can contact Bravehearts on 1800 272 831 or Blue Knot on 1300 657 380. Lifeline is available 24 hours a day on 13 11 14.