The GS per Triangle Invocations metric represents the number of geometry shader invocations. The value is 0 if no geometry shader is associated with the rendering call.
If GS Per Triangle Invocations is 1000, it means that the geometry shader was invoked for 1000 primitives.
The only way to minimize the number of geometry shader invocations is to minimize the number of input primitives. The impact on rendering performance of reducing the invocation count is highly dependent upon your specific game or application.