The contract for a game always contains a guarantee payment to the visiting team. Smaller colleges often fund their entire athletic department from these guarantees when they play Power-5 teams, but I don't think the guarantee involves a specific cut of the television revenue.
Whenever ND plays a road game, the contract provides them with a rather large guarantee payment. How the home team gets the money to pay Notre Dame or any visitor is entirely up to the home team - thus some of the guarantee that a Purdue or a Michigan State pays Notre Dame might very well come from their cut of the Big Ten television money. But the contract does not specify that Notre Dame gets a percentage of the television money - the contract simply contains a guarantee dollar amount that is to be paid to the visiting team.