You are thinking about and approaching this wrong.
You actually NEED some reflections in the glass to "define" a clear object. Without some reflections, it will virtually disappear and at best appear two dimensional.
For example, the following image was shot with a big, white softbox on one side of the object and a large black flag opposite, both of which reflect in the clear glass to define the shape of the object and to give a more three-dimensional impression...
Another example, this time with the subject set on a translucent light table and illuminated from below to define the shape and three-dimensionality of the object...
A Circular Polarizing filter can used to control some reflections. In the below example - done by window light, with reflectors - a C-Pol was used carefully so that the transparent packaging was apparent, but the product inside was still fully visible...
In fact, it's the same with a reflection in a person's or animal's eye... A "catch light" is important to make an animal look alive and vital. Without it they'll look artificial, inanimate...
"Eliminating reflections" from the glass vase would also eliminate the catch light in the cat's eyes.
In other words, don't try to ELIMINATE the reflections... USE THEM! They're important aspects of the image.
BTW: Both your example images are at least a full stop under-exposed. Why are you using ISO 200. With a D750 should be able to shoot at least ISO 800 without any noise issues. That might also allow you to stop the lens down to f/4 or f/5.6 (in your first example, the painting on the wall and it's frame are slightly "soft" due to shallow depth of field... while the cat, vase and flowers in front of them are nice and sharp... but maybe that was intentional). Under-exposure leads to noise when you have to boost exposure in post-processing. To minimize noise, you're usually better off slightly over-exposing and "pulling" image exposure back down a little (1/3 to 1/2 stop, max).
Yours is a very cooperative cat!