QPR are also due some revenge from Town after snatching a last minute winner in the league last month, against the run of play.
Grove is hoping a cup run can breathe some confidence into league performances.
Because we had a 3-1 defeat at Rushden and we're playing at home against a decent side who have beaten us here, it puts a bit more edge on the game," Groves told the Grimsby Telegraph.
"The result last week rankles us a bit. We want to get revenge on QPR and atone for that result last week. That all adds more spark to the game.
"But this game has the potential to give us a boost. Because of the type of side we're playing - they're near the top of our league - if we get the right result it could get us back on track and help us start winning games.
"Good Cup runs can breed confidence and kick-start you and we're no different, especially with our performances of late.
"We need more of a return from a points aspect. From this game we need an end product and that means getting into the next round.
"We are where we are in the table and there are reasons for that. We're looking to improve and get up the table and this can help."