The Cats thought long and hard about the decision on Tuesday morning, but they are adamant that Johnson's contact with Thompson did not involve enough force to warrant a report.
They believe their gun midfielder should be cleared to line up in Saturday night's blockbuster clash with Fremantle at Simonds Stadium.
Speaking before the decision to contest the charge was made, Geelong coach Chris Scott said he was "shocked" that Johnson had been offered a one-match ban by the Match Review Panel.
"But my views and my reaction was probably the same as most other reasoned people within the football industry," Scott added.
Johnson's poor record means he will be banned for two matches if he failed to have his latest suspension overturned.
But the Cats are adamant that he should be cleared.
"My position is that we would have to be absolutely adamant that there's been a travesty of justice here for us to even consider risking losing Steve for another game," Scott said.
"Given the fact that there was a 300-game umpire two metres away, and he didn't see the need to even pay a free kick, then I think that would work strongly in our favour," Scott said.
"The way the system works, for us to plead our case on this one, in what is a very innocuous incident, we have to risk Steve not only missing the biggest game of the season for us this week, but missing a really big game the week after for something that is, in the way footy's played, absolutely inconsequential."
Although Johnson has been suspended a number of times in recent years, Scott is not holding him to account for the incident with Thompson.
"We're looking at this incident right at the moment absolutely in isolation, which is only fair to Steve," Scott said.
"On viewing the incident and taking into consideration all the issues, then anger towards Steve is not on my agenda at the moment."
As for whether the Match Review Panel system should be reviewed, Scott said: "I think the prevailing view across the competition at the moment, if I'm reading it accurately, is that given some of the other incidents across the weekend, the Steve one doesn't meet scrutiny.
"We don't live in a vacuum. We can't just isolate the Steve Johnson incident from this weekend. We've got to look at it in comparison to others.
And when we talk about sufficient force to constitute a reportable offence, and have one of the best players in the competition missing his club's biggest game of the year, then it's only fair that you have a look at other incidents across the weekend.
"According to other people in the industry, these decisions do not stand up to scrutiny.
"I will leave it to the other people within the industry to argue that one on our behalf. And I think I said this 12 months ago, but the system will be reviewed at the end of the season."
Chris Scott discusses the Johnson report
