Hull official Carl Boyeson did agree to view the video and wipe out the suspension if he felt he made the wrong decision.
Grovre revealed that the referee's assessor backing the appeal but nothing will come of it.
"We've spoken to the assessor and he's agreed that it's debatable whether Marcel should have got a yellow card or nothing," a bitter Groves told the Grimsby Telegraph.
"The assessor is inclined to agree with us. But it's a case that it doesn't affect anybody else so no-one cares.
"It's hard luck to us and that's the end of it."