Hodge felt Ginnivan went too far in his by-play with ex-Collingwood teammate Brodie Grundy when he responded to a post with a public "see you in 14 days" response.
It was a reference to a possible preliminary final meeting between Grundy's Sydney Swans and the Hawks, who must beat the Power at Adelaide Oval on Friday night to advance.
"One thing you don't do is give ammunition to the opposition," Hodge said on SEN radio.
"He's having a bit of a joke, he played two years with Grundy at Collingwood, so they know each other and it's probably a bit of banter.
"But what you do is you send banter in a text message, you don't put it out in the open for Port Adelaide to sit there and go, 'Let's use this and get stuck into Ginnivan'."
View this post on Instagram A post shared by Brodie Grundy AFL (@brodiegrundy)
Ginnivan's post came a few days after he raised eyebrows by going out for dinner at a popular Richmond pub the night before the Hawks' elimination final win over the Western Bulldogs.
Mitchell had no issue with Ginnivan's pub trip and wasn't overly concerned by the social media post.
"Hodgey's obviously from my old-school days," Mitchell said on Wednesday when asked about his four-time premiership teammate's comments.
"I heard his comments and I know that he's just trying to spur on the Hawks as he goes for us this week.
"I'm not sure about motivating Port Adelaide. They've got their season on the line the same way we do.
"We're going into a knockout final and I think both teams are going to be as highly motivated as you could possibly hope for.
"I don't buy into too many things outside that."
Mitchell faces a selection dilemma after key defender Sam Frost was ruled out for the rest of the finals series with a foot injury, with pre-season pick-up Ethan Phillips presenting a tall option.
But the 25-year-old has played just one senior game, when the Hawks coughed up a big lead away to Port in their most recent meeting back in May.
Hawthorn tall Sam Frost in action against the Bulldogs, his last game of the season due to injury. (Joel Carrett/AAP PHOTOS)
Jai Serong and rebounding defender Changkuoth Jiath are also in the mix, and all three trained with the Hawks' main group at Waverley Park on Wednesday.
Jiath missed the final three games of the home-and-away season with calf tightness but has since proved his fitness at VFL level.
"You're a little bit torn. You obviously can't replace exactly Sam Frost - he's been so important for us and he's had a fantastic season," Mitchell said.
"Even the way he's handled the last few days: he's been in every meeting, he's helping with the preview and helping with what works and perhaps doesn't against some of the Port Adelaide guys.
"Trying to replace everything about Sam Frost is not going to be done but we need to bring another player in.
"There's a bit of flexibility in the team so there's a few things that we can do, whether it's move someone from another position back and bring someone else in or go like-for-like."
