Service Fee/tipping Caterers

Our wedding will be at a vineyard venue where the venue will be providing the alcohol and the caterer will be only managing food. We are doing a sit down dinner with a salad and main entree.
Our caterer already has a 15% administrative charge in the contract. It states “our administrative fee of the cost of food and beverage and is retained by the restaurant as an administrative fee to help offset various costs associated with the event (e.g. equipment expenses, facilities expenses, insurance, etc) and is not a gratuity or shared with the staff.
Our plates are $88/pp and we have almost 175 people, so this admin fee is $2000+. There is also a state sales tax applied to the total bill.
Considering that, what would be an appropriate amount to tip the caterers? I have seen all different ranges online.