Open the file in photoshop

Choose select>color range

Use the eyedropper and drag it along the full range of the grey background color

Click enter

Now, the background is selected
choose select>feather and try 2 pixels

Open the file in photoshop

Choose select>color range

Use the eyedropper and drag it along the full range of the grey background color

Click enter

Now, the background is selected
choose select>feather and try 2 pixels