Which Menu Book are you encountering this problem with?
Tyres come in three grades: Comfort, Sports, and Racing, and each grade has three levels of softness, from Hard, Medium, and Soft. If you've bought Sports Hard tyres, it may be that the event requires Racing Hard tyres, or (very unlikely) Comfort Hards.
A neat trick to revert your car to its default tyres is to create a new tuning sheet in the car settings. Most likely, the event you're trying to get into requires the car's default tyres; not many Menu Books require tyres different from what the car originally comes with from my memory.
It's important to note that buying tyres from the tuning shop (Understeer) will equip the parts automatically upon purchase, but buying tyres from the race menu (N2O) will not. To check what tyres your car currently has, go to car settings.
Try creating a new setting sheet OR fitting Racing Hard tyres, see if that fixes your problem.