The definition of gravitational field strength states: gravitational field strength is the force experienced per unit mass by a small test mass at a point in gravitational field. It can be given as $g = (GM)/r^2$, I don't understand why the statement has to mention it is "the force experienced per unit mass by a small test mass." Why can't it be "the force experienced per unit mass by a test mass." Here is my thought on this: by nature, the universal gravitational force can be seen as a pair of action and reaction force between two mass by newton's third law, the greater mass is seen as the one providing the action force ,or in another word, the gravitational field, hence the definition of gravitational field strength is given in the "provider's perspective". Can some one help me on this?
You are defining the gravitational field strength at a point.
If an extended test mass is used then the each part of the test mass might experience a different gravitational field strength in a region where the gravitational field strength is not necessarily constant.
Update as a result of a comment by the OP
Does the object with greater mass always provide action force or is my interpretation wrong?
Assigning the words action and reaction to forces should not be interpreted as one force being more important than the other ie you cannot say that it is because a body is more massive that it creates a force on on a less massive body which in turn is forced to create a force on the more massive body.
You could equally have said that the less massive body exerts a force on a more massive body which in turn is forced to create a force on the less massive body.
Rather than use the words action and reaction it is perhaps better to call the forces; the force on the more massive body due to the less massive body and the force on the less massive body due to the more massive body or the force on body $A$ due to body $B$ and the force on body $B$ due to body $A$.
Having read this you will perhaps realise that using the words action and reaction is much simpler and less verbose and using the words action and reaction as labels to the two forces is easier.
Perhaps the idea that the more massive object provides the action force comes from the fact that often only one of the two forces are considered.
For example when considering an object falling towards the Earth on the force on the object (action!) is consider to cause an acceleration.
There is of course a reaction!, the force on the Earth due to the object, but as the mass of the Earth is so much larger than that of the object the acceleration of the Earth is ignored.