United face their first Ladbrokes Premiership opposition since their relegation when they visit the Tulloch Caledonian Stadium in the Betfred Cup on Saturday.
Ray McKinnon’s new-look side dropped a point in their opener at Arbroath but hit four first-half goals in a 6-1 victory over Cowdenbeath in midweek.
Tremarco told Caley Jags TV: “They will think because we are the Premiership side - it still sounds a bit strange actually saying it to be honest - but they will want to take a scalp. And they used to be the ones getting hunted.
“It will be interesting. I am sure they will be coming here with confidence on the back of that 6-1 victory.”
Tremarco, whose side opened with a 2-1 win at Cowdenbeath, added: “It will be interesting to see how they have made the transition from being in the Prem to the Championship. Looking at the team the other day, there are a fair few players who are still there.
“But it’s all about what we do on the park. We know they gave Cowdenbeath a bit of a hiding the other night, but to be fair if we had taken our chances on Saturday then it would have been the same score.
“So I’m not going to read too much into that. We will just focus on us, we are not really worried about them to be honest.”
Caley Thistle manager Richie Foran has a minor doubt over goalkeeper Ryan Esson (groin) but expects him to make the game. First-choice Owain Fon Williams is still to return after being handed extra time off following his Euro 2016 exploits with Wales.