How can I get rid of the white layer drawn under the bitmap images by Delphi/Windows when Glyph property of TBitBtn is used. I just want to draw the image, no shadow under it, no other layers that comes automatically. I am inserting round shaped 24 bit bitmap images.

Since you have a 24-bit bitmap, there is no alpha transparency, so Delphi uses the bottom left pixel of the image to determine the transparent color. All pixels with that color are treated as transparent. The part of the image with the shadow effect is not an exact match for the designated transparent color, so those pixels are painted normally, just like the rest of the image.
The shadow appears white because there was a white background in the graphic program when your designer applied the shadow effect.
Either edit the image to remove the shadow, or use a 32-bit image with alpha transparency. You’ll be hard-pressed to apply alpha transparency after the fact. Fix the source image.