When you wish to remove the background from an image, if you need to remove the background in a very precise manner, its better to use the clipping tool inside Photoshop vs an online background removal software.
When you click on the clipping tool, you can trace out the specific part of the photo you wish to keep and Photoshop will remove the other parts of this image.
Here is a simple before and after photo of how an image would look like after using the clipping tool inside Photoshop.