Lots of incorrect information on here about how eventing tack checks are done…
At national level events bits/bridles/spurs/whips are checked for every rider - can be done before or after test…but unless there’s been something said by the officials to waive tack checks for that event, it’s done for every rider. Bridles are not required to be removed from the horse’s mouths…during COVID bits were checked via visual inspection. Otherwise it’s a gloved finger in the horse’s mouth. A rider could choose to have the bridle removed but it’s by far the exception rather than the rule. Bonnets are pulled by the rider or groom, but mostly with the bridle left on.
There is no required bit check after XC. Bridles you see being removed on the livestream of big events are because the horses are being stripped down in the vet box to be cooled out…and will go back to the barn in a halter. Occasionally you may see a bridle removed after the finish for a horse to be led back in hand…but this is not because there’s any kind of tack check being done.
At FEI events, after dressage the bit check is done by an appointed FEI steward. The horse is ridden from the ring to that area for the check to be done. The grooms cannot touch the horse during this time. At the equipment check the bridle is most often not removed - the FEI officials can check the bits with gloved hands as well. Bonnets are pulled, but usually without removing the bridle. Tack checks after the showjumping phase are to check boots and weigh them.