Danny Wilson’s side are aiming to become the competition’s first new finalists since La Rochelle in 2021, but face a tough challenge – they were hammered by Toulouse at home in December during the pool stage.
However, in their quarter-final against Bordeaux, they also went in as heavy underdogs and produced one of the great European away performances.
Victory for Wilson’s side would set up at final at Tottenham Hotspur Stadium on 25 May against Leinster or Northampton Saints, who play on Saturday at Croke Park.
“No-one is going to give us any hope and we are fine with that. It was the same with the guys in Bordeau – not many thought we could do anything down there apart from a few Quins fans and some of the players,” Care added.
“Everyone will be saying it is Toulouse against Leinster or Northampton in the final and that is fine. We are happy with that.”