Step 1: Recall the operation of a solid rocket motor.
In a solid rocket motor, the fuel and oxidizer are premixed in the propellant grain.
Unlike liquid rockets, there are no injectors or turbopumps to regulate the flow.
Step 2: Determine what controls the thrust.
The thrust depends mainly on the propellant burning rate and the exposed burning surface area.
These are governed by the grain geometry.
Hence,
\[
\boxed{
\text{Thrust is primarily controlled by the grain geometry and burning surface area.}
}
\]
Therefore,
\[
\boxed{(C)}
\]
is the correct answer.