Checkered logo to T-shirt mockup

@Muhammad Sattar 

PNGs support only one layer, so the gray and white squares are now part of the one layer.

If your client created the artwork in Illustrator or another vector application and saved it as .ai or .eps, you could open the file in Illustrator. There you could turn off or delete the layer with the squares. (Best choice)

If you expanded the layer in Illustrator, you would see that the background is composed of grey and white squares. You said your client wants to keep the checked background. To do that, you would simply create more squares. Note that others will think this was a mistake.

I have to say that I have never seen a client create a layer with the squares before. I've only seen it in stock images where the creator uses this method to indicate transparency IF the file is opened in Illustrator or another vector application. Opening it in Photoshop rasterizes it.

Ask your client for the original file in .ai or .eps format, then hide, delete, or expand the individual squares there.

Jane