Is grip force a reflex?
holding an object is usually a task that requires visual and mechanical processing (i.e. what the object looks like (i.e. what material does it seem to be made of, what is your former experience with that material, how heavy does it feel) and muscle memory.
according to the physiological definition of a reflex:

Reflex, in biology, an action consisting of comparatively simple segments of behaviour that usually occur as direct and immediate responses to particular stimuli uniquely correlated with them.

according to this same source, innate reflexes such as walking, blinking and swallowing require skeletal muscles but are still considered reflexes despite the fact that for some of these tasks (such as walking and standing) we do not know from birth (meaning reflexes can be taught and unlearned/lost).
There are other reflexes such as intestinal smooth muscle contractions etc... that we are usually completely unaware of and are controlled by the central nervous system (CNS) unconsciously.
The response to pain is also a reflex; the thermal/mechanical neural sensors in your arm (for example) send the information to your spine which directly sends a signal to your muscles to contract in order to avoid/release the object.
the palmar grasp reflex is one of many reflexes babies have that they do not need to be taught. Adults usually unteach these reflexes as some of them are not as frequently necessary in later stages of life. Newborn apes for one use the palmar grasp reflex to hold on to their mothers (it is possible that is where that reflex came from from an evolutionary standpoint).
consider that all reflexes are caused by cues that your nervous system senses and responds to. Some of these reflexes can be controlled and others not and may vary depending on your environment. A famous example of this is the pavlov's dog experiment which proved that you could also be conditioned to respond to a certain stimulus. In your case, seeing or feeling the cup is supposed to provide a stimulus to your brain reminding you that you are holding an object that requires a specific mechanical maneuver which you have learnt over time.