Scrum-half Murray hit out at Glasgow's "very dangerous" attempts to take out his standing leg when kicking back in a European clash in January 2017.
Scotland have continually tried to unsettle Ireland's stellar British and Irish Lions playmaking duo, and Murray's Munster team-mate O'Mahony fully expects more of the same in Yokohama this weekend.
"Look, it hasn't come into our thinking. It's a Test game, half-backs are always targeted," O'Mahony said.
"Jacob's already spoken about Finn Russell. If you can get to the other team's playmakers it gives you advantage and that isn't something that's new in Test rugby.
"And it isn't going to be any different tomorrow. So front-foot ball, solid set-piece, having the ability to get ourselves into the game and starting well is paramount for us.
"So Johnny and the boys are well able to look after themselves."
The 59-cap flanker O'Mahony said Ireland had been waiting for this World Cup to kick-off for so long their eagerness for a strong start had hit fever pitch.
Ireland suffered a record 57-15 loss to England at Twickenham just last month, but rebounded with back-to-back victories over Wales.
Joe Schmidt's side enter this tournament as the world's number-one ranked team. But while New Zealand remain the bookmakers' favourites for a third World Cup triumph in succession, Ireland are itching to make good on their vows to hit their peak at exactly the right time.
Asked if Ireland, and especially the forwards, were ready to hit new heights in Japan, O'Mahony said: "I think you have to think you're ready, you've been waiting for this for a long time.
"It's the game everyone's been waiting for. And 18 months ago we spoke about it briefly, but when you're playing big tournaments it kind of catches up with you. All of a sudden you're into the World Cup pre-season.
"But now it's here, and it's the one where everyone wants to start well and perform well.
"We've had a great pre-season and you have to think and believe we're ready to go."
O'Mahony said Ireland had been "taken aback" by the depth of the welcome from the Japanese public.
The 30-year-old said Ireland would now aim to take that feel-good factor into their World Cup bid.
"We're a very proud nation, a proud squad; to be from Ireland and to get an opportunity to play for Ireland is something that no one takes lightly," said O'Mahony.
"Whether you're in the 31, 23, or starting fifteen, it's a huge honour to be here playing in a World Cup in Japan.
"That's the overwhelming thing, with regard to the team, we've had a fabulous welcome from the Japanese people and we're certainly very grateful for that.
"I was lucky enough to be here 10 years ago and experience a lot of the cultures here.
"But the welcome this time has been absolutely incredible, and a lot of the guys have been taken aback by that.
"We'd consider Ireland a very welcoming country, but Japan take that to a different level."
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