Reversing the Direction of An Induction Motor?
In order to reverse a single-phase motor, it is usually necessary to reverse one winding with respect to the other. If you don't have access to both ends of the windings, the motor can not be reversed. That is likely the case for a dryer.

Some motors that are designed for reverse operation have two identical windings. In that case, the capacitor can be connected to either winding for either direction. That is certainly not the case for a dryer.

If the motor runs in the "wrong" direction for its original use, the capacitor may now be connected to the "wrong" winding.