Groundwire issues for floodlight

I have a ring wired floodlight i want installed outside my house. If you look at the pictures you can see I don’t have a typical junction box set up. Instructions with the floodlight tell me I must not connect the ground wire to the metal mounting bracket included with the light. But the groundwire is currently screwed into a separate metal bracket along the side of my house. Obviously the ground wire is not connecting to the floodlight And should be secured under the green screw. However, with the way the groundwire is set up right now, is that going to cause problems for me if i try and take the other end of that wire and tuck it under the screw? Or is it only the metal mounting bracket included with my floodlight that the groundwire cannot touch?