Smooth Camo Overlay for TG Logo

I need help overlaying a camouflage design onto our company TG logo while maintaining the exact dimensions and size of the original logo. The issue I’ve encountered is with the inside of the 'G', where the edges are not smooth. I am providing the camouflage pattern that I want to be used as the fill.

The goal is to focus on specific sections of the attached camouflage to create the best visual effect inside the TG logo. The final design must have smooth and seamless integration of the camouflage within the logo's shape. If you’re skilled in precision design and can ensure a refined finish, I’d love to work with you on this project.