You can use the magic wand tool to select the white/grey back ground. Make sure to adjust your tolerence in the settings.
If you want to adjust your selection, you can either use the scribble selection tool or the brush selection tool. If you want even more precise selection of the background, I would suggest importing the project into Adobe Photoshop on a computer to further refine it. Hope this helps!
Have you tried using the paint selection tool or the scribble selection tool to mask out the reflection of the glasses along with the glass frame? If you want you can bring the image into Photoshop and create masks for them.
Lightroom would be faster and more efficient for batch adjustments if you are not using any masks for the frame and its refleciton.