mat

go to the mat vigorously engage in an argument or dispute, typically on behalf of a particular person or cause.

☞ The mat referred to is the thick mat in a gym on which wrestling is practised.

1924P. G. WodehouseLeave it to Psmith I…heard…you and Aunt Constance going to the mat about poor old Phyllis.

on the mat being reprimanded by someone in authority. informal

☞ This idiom is a military reference: the orderly room mat was where a soldier accused of some misdemeanour would stand before the commanding officer.