When a force is exerted on an object, does a large force always produce a larger change in the object's momentum than a small force does?

Yes, it is true

Explanation:

According to the Newton's second law, the force applied on a body is directly proportional to the rate of change of momentum of the body.

F ∝ dp/dt

Where, dp is the change in momentum in time dt.

So, if the time of change in momentum is same, a large force is applied on the body, it means a large change in momentum of the body.

if a small force acting on the body it means a small change in the momentum of the body.