Reflections are part of what makes glass look like glass. The issue is not so much with the material (making a shader with no reflections completely is quite easy, but will make the glass look like there is no surface at all).
Look at images of watches and do a search on how to photograph them. The important thing that you will notice is how the surrounding elements play a crucial role in the scene. You want reflections that show the glass, but you want also some black (or dark) elements reflected on the surface that make the transparency more evident. So you have to be strategic about how objects and lights are placed around the watch.
Read: How to turn off reflections on glass
Also, when dealing with elements behind glass, the thickness of the glass will play a crucial role. If the glass has no thickness (like a a plane) then the glass material will behave like a single glass solid, as if the insides were encapsulated completely in a glass block instead of being behind a thin piece of glass. The glass has to have a realistic thickness.
To create a shader for elements behind glass in cycles read:
How to illuminate the darkness inside glass objects in Cycles?
Objects behind glass appear too dark
As a final note: a plain HDR of trees as environment is not the optimal way to light a scene like yours.