This is also being discussed in gameplay discussion forum:

Discussed in the live chat on Jan 5th, but since nothing seems to get done unless there is a bug thread, here it is.

The quest, Challenge: Cordial Delivery, is not longer available at the quest giver. Originally you could pick it up and try it whenever. Tried to do it on my donkey many times. Now no quest, and this quest further blocks two other quests.

Now however it will not give a quest. Apparently one of the B200 cars will give you a quest to deliver a fresh Cordial to the quest giver which then opens up this quest. None of the other B200 cars, other cars, or steam bike gets this quest.

I believe it must be a bug to lock 3 fun quests and their titles to only a specific pay to win car.