Keep the 'g'. The current logo is clear, easily identifiable and works well at small scales. It's important to consider whether the suggested changes will negatively affect accessibility or possibly even violate US ADA guidelines.
Keep in mind that these logos and icons need to work equally effectively everywhere. It needs to work on very large screens, very small screens and at all different scales and in high contrast modes and inverted colour modes and greyscale modes and so on and so forth.
